957:
52:
832:. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include
1298:), gradually a belief formed that nearly all finite simple groups can be accounted for by appropriate extensions of Chevalley's construction, together with cyclic and alternating groups. Moreover, the exceptions, the
1848:. To see this for any particular order is usually not difficult (for example, there is, up to isomorphism, one non-solvable group and 12 solvable groups of order 60) but the proof of this for all orders uses the
1143:
An arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants. The
497:
472:
435:
1646:
The proof of the theorem consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004.
799:
2482:
2452:
2385:
2355:
1849:
1572:
1310:
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1635:
is that such "building blocks" do not necessarily determine uniquely a group, since there might be many non-isomorphic groups with the same
1155:
and later was both simplified and generalized to finitely generated modules over a principal ideal domain, forming an important chapter of
1147:
of a finite abelian group can be described directly in terms of these invariants. The theory had been first developed in the 1879 paper of
1690:
1339:
913:
of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of
307:
2370:
792:
302:
1385:
This provides a partial converse to
Lagrange's theorem giving information about how many subgroups of a given order are contained in
1290:. Moreover, as in the case of compact simple Lie groups, the corresponding groups turned out to be almost simple as abstract groups (
863:
During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the
1302:, share many properties with the finite groups of Lie type, and in particular, can be constructed and characterized based on their
1247:
1231:
1631:
is a more precise way of stating this fact about finite groups. However, a significant difference with respect to the case of
2552:
718:
1619:
The finite simple groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the
2666:
2390:
1651:
1501:
785:
1628:
2365:
1758:
1710:
1576:
1258:â 2, 3. This theorem generalizes to projective groups of higher dimensions and gives an important infinite family PSL(
402:
216:
1434:
1822:
600:
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211:
99:
1129:
1097:
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1190:
750:
540:
2410:
1632:
1368:
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implies that the cyclic subgroup generated by any of its non-identity elements is the whole group. If
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1540:
1471:
1349:
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is the square of a prime, then there are exactly two possible isomorphism types of group of order
480:
455:
418:
2585:
2440:
2360:
1636:
1144:
124:
96:
1294:). Although it was known since 19th century that other finite simple groups exist (for example,
1239:
1317:
include all the finite simple groups other than the cyclic groups, the alternating groups, the
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2548:
2466:
1647:
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1137:
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give asymptotically correct estimates for the number of isomorphism types of groups of order
1218:
Finite groups of Lie type were among the first groups to be considered in mathematics, after
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1212:
1208:
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since it arose in the 19th century. One major area of study has been classification: the
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75:
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1313:. Inspection of the list of finite simple groups shows that groups of Lie type over a
2655:
1706:
1407:
1133:
1116:
1100:
gives an isomorphism between the two. This can be done with any finite cyclic group.
1081:
925:. These are finite groups generated by reflections which act on a finite-dimensional
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446:
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185:
1686:
1682:
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in the 1830s. The systematic exploration of finite groups of Lie type started with
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80:
43:
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829:
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440:
17:
1024:
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533:
929:. The properties of finite groups can thus play a role in subjects such as
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1422:
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910:
70:
1658:
are gradually publishing a simplified and revised version of the proof.
886:
During the second half of the twentieth century, mathematicians such as
2375:
1504:
898:, and other related groups. One such family of groups is the family of
412:
326:
1724:, some restrictions may be placed on the structure of groups of order
1278:
realized that after an appropriate reformulation, many theorems about
1080:, the identity. A typical realization of this group is as the complex
2634:
sequence A060689 (Number of non-Abelian groups of order n)
1065:
is a group all of whose elements are powers of a particular element
1132:
to two group elements does not depend on their order (the axiom of
2630:
2618:
2610:
1825:, which has a long and complicated proof, every group of order
2622:
sequence A000688 (Number of
Abelian groups of order
2445:"The Status of the Classification of the Finite Simple Groups"
1864:
for which there are two non-isomorphic simple groups of order
1282:
admit analogues for algebraic groups over an arbitrary field
1717:, and the number grows very rapidly as the power increases.
2633:
2621:
2613:
1888:
1884:
1880:
1792:
is divisible by fewer than three distinct primes, i.e. if
1670:, it is not at all a routine matter to determine how many
883:
from which all finite groups can be built are now known.
27:
Mathematical group based upon a finite number of elements
2639:
2614:
sequence A000001 (Number of groups of order n)
1728:, as a consequence, for example, of results such as the
1203:. Finite groups of Lie type give the bulk of nonabelian
843:
The study of finite groups has been an integral part of
1519:
has order divisible by at least three distinct primes.
2473:, December 1, 1985, vol. 253, no. 6, pp. 104â115.
894:
also increased our understanding of finite analogs of
483:
458:
421:
1215:, the Steinberg groups, and the SuzukiâRee groups.
1016:from the set of symbols to itself. Since there are
1860:, and there are infinitely many positive integers
491:
466:
429:
1286:, leading to construction of what are now called
1035:(the number of elements) of the symmetric group S
1757:. For a necessary and sufficient condition, see
1615:(sometimes considered as a 27th sporadic group).
1274:in the beginning of 20th century. In the 1950s
1705:is a higher power of a prime, then results of
1433:. This can be understood as an example of the
2547:. Oxford University Press. pp. 238â242.
2483:Group Theory and its Application to Chemistry
2456:. Vol. 51, no. 7. pp. 736â740.
1856:there are at most two simple groups of order
793:
8:
2453:Notices of the American Mathematical Society
1560:
1556:
921:", is strongly influenced by the associated
1012:of such permutations, which are treated as
909:Finite groups often occur when considering
1579:belongs to one of the following families:
1309:The belief has now become a theorem â the
1128:in which the result of applying the group
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238:
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29:
1270:. Other classical groups were studied by
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1720:Depending on the prime factorization of
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917:, which may be viewed as dealing with "
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122:
32:
2386:Representation theory of finite groups
2356:Classification of finite simple groups
1850:classification of finite simple groups
1573:classification of finite simple groups
1567:Classification of finite simple groups
1311:classification of finite simple groups
877:classification of finite simple groups
849:classification of finite simple groups
358:Classification of finite simple groups
1623:are the basic building blocks of the
879:was achieved, meaning that all those
7:
1732:. For example, every group of order
1189:) of rational points of a reductive
1027:) possible permutations of a set of
1784:, states that every group of order
867:of finite groups and the theory of
1872:Table of distinct groups of order
1821:are non-negative integers. By the
875:. As a consequence, the complete
25:
1662:Number of groups of a given order
1643:does not have a unique solution.
1340:Lagrange's theorem (group theory)
1234:over prime finite fields, PSL(2,
2485:The Chemistry LibreTexts library
2469:(1985), "The Enormous Theorem",
1701:, both of which are abelian. If
1575:is a theorem stating that every
1232:projective special linear groups
50:
2371:Cauchy's theorem (group theory)
1248:projective special linear group
1367:. The theorem is named after
1352:(number of elements) of every
1181:closely related to the group
719:Infinite dimensional Lie group
1:
2391:Modular representation theory
1207:. Special cases include the
1031:symbols, it follows that the
2366:List of finite simple groups
1639:or, put in another way, the
492:{\displaystyle \mathbb {Z} }
467:{\displaystyle \mathbb {Z} }
430:{\displaystyle \mathbb {Z} }
2543:Humphreys, John F. (1996).
1852:. For any positive integer
1836:For every positive integer
1535:, states that every finite
996:whose elements are all the
217:List of group theory topics
2683:
1878:
1772:, then any group of order
1681:there are. Every group of
1452:
1396:
1378:
1337:
1166:
1107:
1052:
949:
851:(those with no nontrivial
2648:for groups of small order
2580:Jacobson, Nathan (2009).
1666:Given a positive integer
1515:. Hence each non-Abelian
855:) was completed in 2004.
2545:A Course in Group Theory
1599:simple group of Lie type
1136:). They are named after
335:Elementary abelian group
212:Glossary of group theory
1840:, most groups of order
1813:are prime numbers, and
1448:
1392:
1333:
1292:Tits simplicity theorem
1238:) being constructed by
1098:primitive root of unity
964:of the symmetric group
1606:sporadic simple groups
1323:sporadic simple groups
1306:in the sense of Tits.
1191:linear algebraic group
971:
751:Linear algebraic group
493:
468:
431:
2411:Commuting probability
1823:FeitâThompson theorem
1633:integer factorization
1629:JordanâHölder theorem
1594:of degree at least 5;
1529:FeitâThompson theorem
1523:FeitâThompson theorem
1470:is a finite group of
1406:, named in honour of
1369:Joseph-Louis Lagrange
1363:divides the order of
1344:For any finite group
1280:semisimple Lie groups
1104:Finite abelian groups
959:
900:general linear groups
494:
469:
432:
2667:Properties of groups
2416:Finite State Machine
2381:List of small groups
1553:John Griggs Thompson
1410:, states that every
1268:finite simple groups
1246:'s theorem that the
1205:finite simple groups
1153:Ludwig Stickelberger
1110:Finite abelian group
481:
456:
419:
2533:, p. 72, ex. 1
2471:Scientific American
2441:Aschbacher, Michael
2396:Monstrous moonshine
1674:types of groups of
1577:finite simple group
1547:. It was proved by
1517:finite simple group
1441:on the elements of
1196:with values in the
1014:bijective functions
1004:symbols, and whose
931:theoretical physics
919:continuous symmetry
125:Group homomorphisms
35:Algebraic structure
2586:Dover Publications
2361:Association scheme
1778:Burnside's theorem
1691:Lagrange's theorem
1637:composition series
1460:Burnside's theorem
1455:Burnside's theorem
1449:Burnside's theorem
1334:Lagrange's theorem
1163:Groups of Lie type
1145:automorphism group
972:
946:Permutation groups
838:permutation groups
601:Special orthogonal
489:
464:
427:
308:Lagrange's theorem
2595:978-0-486-47189-1
2467:Daniel Gorenstein
2346:
2345:
1829:is solvable when
1788:is solvable when
1753:not divisible by
1641:extension problem
1592:alternating group
1587:with prime order;
1533:odd order theorem
1230:groups, with the
1175:group of Lie type
1169:Group of Lie type
1138:Niels Henrik Abel
1122:commutative group
952:Permutation group
810:
809:
385:
384:
267:Alternating group
224:
223:
16:(Redirected from
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2638:Small groups on
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2584:(2nd ed.).
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1782:group characters
1752:
1746:are primes with
1745:
1404:Cayley's theorem
1399:Cayley's theorem
1393:Cayley's theorem
1288:Chevalley groups
1276:Claude Chevalley
1254:) is simple for
1213:Chevalley groups
1209:classical groups
1120:, also called a
1089:
1088:
1079:
1059:A cyclic group Z
896:classical groups
873:nilpotent groups
814:abstract algebra
802:
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744:Algebraic groups
517:Hyperbolic group
507:Arithmetic group
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291:Quaternion group
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2582:Basic Algebra I
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2573:Further reading
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2401:Profinite group
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1891:
1879:Main articles:
1877:
1793:
1780:, proved using
1747:
1737:
1736:is cyclic when
1664:
1625:natural numbers
1569:
1549:Walter Feit
1525:
1466:states that if
1457:
1451:
1427:symmetric group
1401:
1395:
1383:
1377:
1342:
1336:
1331:
1300:sporadic groups
1272:Leonard Dickson
1240:Ăvariste Galois
1171:
1165:
1149:Georg Frobenius
1112:
1106:
1086:
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1006:group operation
992:symbols is the
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976:symmetric group
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927:Euclidean space
861:
853:normal subgroup
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765:Abelian variety
758:Reductive group
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1730:Sylow theorems
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1609:
1604:One of the 26
1602:
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1588:
1568:
1565:
1524:
1521:
1453:Main article:
1450:
1447:
1397:Main article:
1394:
1391:
1381:Sylow theorems
1379:Main article:
1376:
1375:Sylow theorems
1373:
1338:Main article:
1335:
1332:
1330:
1327:
1296:Mathieu groups
1244:Camille Jordan
1167:Main article:
1164:
1161:
1157:linear algebra
1108:Main article:
1105:
1102:
1090:roots of unity
1060:
1053:Main article:
1050:
1047:
1036:
979:
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950:Main article:
947:
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942:
939:
860:
857:
826:underlying set
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708:Diffeomorphism
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447:Modular groups
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320:Hall's theorem
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315:Sylow theorems
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280:Dihedral group
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115:Wreath product
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100:direct product
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92:Quotient group
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2662:Finite groups
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2550:
2546:
2539:
2536:
2532:
2531:Jacobson 2009
2527:
2524:
2520:
2519:Jacobson 2009
2515:
2512:
2508:
2507:Jacobson 2009
2503:
2500:
2496:
2495:Jacobson 2009
2491:
2488:
2484:
2479:
2476:
2472:
2468:
2463:
2460:
2455:
2454:
2446:
2442:
2436:
2433:
2427:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2367:
2364:
2362:
2359:
2357:
2354:
2353:
2348:
2341:
2338:
2335:
2332:
2331:
2327:
2324:
2321:
2318:
2317:
2313:
2310:
2307:
2304:
2303:
2299:
2296:
2293:
2290:
2289:
2285:
2282:
2279:
2276:
2275:
2271:
2268:
2265:
2262:
2261:
2257:
2254:
2251:
2248:
2247:
2243:
2240:
2237:
2234:
2233:
2229:
2226:
2223:
2220:
2219:
2215:
2212:
2209:
2206:
2205:
2201:
2198:
2195:
2192:
2191:
2187:
2184:
2181:
2178:
2177:
2173:
2170:
2167:
2164:
2163:
2159:
2156:
2153:
2150:
2149:
2145:
2142:
2139:
2136:
2135:
2131:
2128:
2125:
2122:
2121:
2117:
2114:
2111:
2108:
2107:
2103:
2100:
2097:
2094:
2093:
2089:
2086:
2083:
2080:
2079:
2075:
2072:
2069:
2066:
2065:
2061:
2058:
2055:
2052:
2051:
2047:
2044:
2041:
2038:
2037:
2033:
2030:
2027:
2024:
2023:
2019:
2016:
2013:
2010:
2009:
2005:
2002:
1999:
1996:
1995:
1991:
1988:
1985:
1982:
1981:
1977:
1974:
1971:
1968:
1967:
1963:
1960:
1957:
1954:
1953:
1949:
1946:
1943:
1940:
1939:
1935:
1932:
1929:
1926:
1925:
1921:
1918:
1915:
1912:
1911:
1907:
1904:
1901:
1899:
1895:
1894:
1890:
1886:
1882:
1875:
1871:
1869:
1867:
1863:
1859:
1855:
1851:
1847:
1843:
1839:
1834:
1832:
1828:
1824:
1820:
1816:
1812:
1808:
1803:
1800:
1796:
1791:
1787:
1783:
1779:
1776:is solvable.
1775:
1771:
1767:
1762:
1760:
1759:cyclic number
1756:
1750:
1744:
1740:
1735:
1731:
1727:
1723:
1718:
1716:
1712:
1708:
1707:Graham Higman
1704:
1700:
1696:
1692:
1688:
1684:
1680:
1677:
1673:
1669:
1661:
1659:
1657:
1653:
1649:
1644:
1642:
1638:
1634:
1630:
1626:
1622:
1621:prime numbers
1614:
1610:
1607:
1603:
1600:
1596:
1593:
1589:
1586:
1582:
1581:
1580:
1578:
1574:
1566:
1564:
1562:
1558:
1554:
1551: and
1550:
1546:
1542:
1538:
1534:
1530:
1522:
1520:
1518:
1514:
1510:
1506:
1503:
1499:
1495:
1491:
1490:prime numbers
1487:
1483:
1479:
1476:
1473:
1469:
1465:
1461:
1456:
1446:
1444:
1440:
1436:
1432:
1428:
1424:
1420:
1416:
1413:
1409:
1408:Arthur Cayley
1405:
1400:
1390:
1388:
1382:
1374:
1372:
1370:
1366:
1362:
1358:
1355:
1351:
1347:
1341:
1329:Main theorems
1328:
1326:
1324:
1321:, and the 26
1320:
1316:
1312:
1307:
1305:
1301:
1297:
1293:
1289:
1285:
1281:
1277:
1273:
1269:
1265:
1261:
1257:
1253:
1249:
1245:
1241:
1237:
1233:
1229:
1225:
1221:
1216:
1214:
1210:
1206:
1202:
1199:
1195:
1192:
1188:
1184:
1180:
1176:
1170:
1162:
1160:
1158:
1154:
1150:
1146:
1141:
1139:
1135:
1134:commutativity
1131:
1127:
1123:
1119:
1118:
1117:abelian group
1111:
1103:
1101:
1099:
1095:
1091:
1085:
1077:
1073:
1068:
1063:
1056:
1049:Cyclic groups
1048:
1046:
1044:
1039:
1034:
1030:
1026:
1023:
1019:
1015:
1011:
1007:
1003:
999:
995:
991:
987:
982:
977:
970:
963:
958:
953:
945:
940:
938:
936:
932:
928:
924:
920:
916:
912:
907:
905:
904:finite fields
901:
897:
893:
889:
884:
882:
881:simple groups
878:
874:
870:
866:
858:
856:
854:
850:
846:
841:
839:
835:
834:cyclic groups
831:
827:
823:
819:
815:
803:
798:
796:
791:
789:
784:
783:
781:
780:
773:
770:
769:
766:
763:
762:
759:
756:
755:
752:
749:
748:
745:
740:
739:
729:
726:
723:
722:
720:
714:
711:
709:
706:
705:
702:
699:
697:
694:
692:
689:
688:
685:
679:
677:
671:
669:
663:
661:
655:
653:
647:
646:
642:
638:
635:
634:
630:
626:
623:
622:
618:
614:
611:
610:
606:
602:
599:
598:
594:
590:
587:
586:
582:
578:
575:
574:
570:
566:
563:
562:
558:
554:
551:
550:
547:
544:
542:
539:
538:
535:
531:
526:
525:
518:
515:
513:
510:
508:
505:
504:
476:
451:
450:
448:
442:
439:
414:
411:
410:
404:
401:
399:
396:
395:
391:
390:
379:
376:
374:
371:
368:
365:
364:
363:
362:
359:
355:
350:
347:
346:
343:
340:
339:
336:
333:
331:
329:
325:
324:
321:
318:
316:
313:
312:
309:
306:
304:
301:
300:
299:
298:
292:
289:
286:
281:
278:
277:
273:
268:
265:
262:
257:
254:
251:
246:
243:
242:
241:
240:
235:
234:Finite groups
230:
229:
218:
215:
213:
210:
209:
208:
207:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
162:
159:
157:
154:
152:
149:
148:
147:
146:
141:
138:
136:
133:
132:
131:
130:
127:
126:
121:
116:
113:
111:
108:
106:
103:
101:
98:
95:
93:
90:
89:
88:
87:
82:
79:
77:
74:
72:
69:
68:
67:
66:
61:Basic notions
58:
57:
53:
49:
48:
45:
40:
36:
31:
19:
18:Finite groups
2623:
2581:
2544:
2538:
2526:
2521:, p. 38
2514:
2509:, p. 41
2502:
2497:, p. 31
2490:
2478:
2470:
2462:
2451:
2435:
1908:Non-Abelian
1897:
1889:oeis:A060689
1885:oeis:A000688
1881:oeis:A000001
1873:
1865:
1861:
1857:
1853:
1841:
1837:
1835:
1830:
1826:
1818:
1814:
1810:
1806:
1801:
1798:
1794:
1789:
1785:
1773:
1765:
1763:
1754:
1748:
1742:
1738:
1733:
1725:
1721:
1719:
1714:
1711:Charles Sims
1702:
1698:
1694:
1678:
1667:
1665:
1645:
1618:
1585:cyclic group
1570:
1532:
1528:
1526:
1508:
1502:non-negative
1497:
1493:
1485:
1481:
1477:
1474:
1467:
1464:group theory
1459:
1458:
1442:
1438:
1435:group action
1430:
1414:
1403:
1402:
1386:
1384:
1364:
1360:
1356:
1345:
1343:
1315:finite field
1308:
1303:
1291:
1287:
1283:
1263:
1259:
1255:
1251:
1235:
1217:
1200:
1193:
1186:
1182:
1174:
1172:
1142:
1121:
1115:
1113:
1093:
1083:
1075:
1071:
1066:
1061:
1058:
1055:Cyclic group
1042:
1037:
1028:
1021:
1017:
1001:
998:permutations
989:
980:
975:
973:
962:Cayley graph
908:
885:
865:local theory
862:
845:group theory
842:
818:finite group
817:
811:
640:
628:
616:
604:
592:
580:
568:
556:
327:
284:
271:
260:
249:
245:Cyclic group
233:
155:
123:
110:Free product
81:Group action
44:Group theory
39:Group theory
38:
2406:Finite ring
1672:isomorphism
1228:alternating
1010:composition
923:Weyl groups
530:Topological
369:alternating
2656:Categories
2646:classifier
2640:GroupNames
2563:0843.20001
2554:0198534590
2428:References
1770:squarefree
1689:, because
1650:(d.1992),
1648:Gorenstein
1613:Tits group
1429:acting on
1419:isomorphic
1319:Tits group
1092:. Sending
986:finite set
915:Lie groups
637:Symplectic
577:Orthogonal
534:Lie groups
441:Free group
166:continuous
105:Direct sum
1902:# Groups
1685:order is
1224:symmetric
1130:operation
1025:factorial
935:chemistry
892:Steinberg
888:Chevalley
701:Conformal
589:Euclidean
196:nilpotent
2443:(2004).
2349:See also
1905:Abelian
1846:solvable
1833:is odd.
1805:, where
1545:solvable
1513:solvable
1505:integers
1480:, where
1423:subgroup
1354:subgroup
1304:geometry
941:Examples
911:symmetry
869:solvable
696:Poincaré
541:Solenoid
413:Integers
403:Lattices
378:sporadic
373:Lie type
201:solvable
191:dihedral
176:additive
161:infinite
71:Subgroup
2376:P-group
1656:Solomon
1627:. The
1555: (
1539:of odd
1507:, then
1425:of the
1250:PSL(2,
1124:, is a
1008:is the
1000:of the
859:History
691:Lorentz
613:Unitary
512:Lattice
452:PSL(2,
186:abelian
97:(Semi-)
2592:
2561:
2551:
1896:Order
1887:, and
1687:cyclic
1654:, and
1492:, and
1348:, the
1220:cyclic
1211:, the
1069:where
830:finite
824:whose
546:Circle
477:SL(2,
366:cyclic
330:-group
181:cyclic
156:finite
151:simple
135:kernel
2448:(PDF)
1741:<
1683:prime
1676:order
1652:Lyons
1541:order
1537:group
1531:, or
1472:order
1421:to a
1412:group
1350:order
1266:) of
1198:field
1179:group
1177:is a
1126:group
1096:to a
1033:order
994:group
984:on a
902:over
822:group
820:is a
730:Sp(â)
727:SU(â)
140:image
2631:OEIS
2619:OEIS
2611:OEIS
2590:ISBN
2549:ISBN
1844:are
1817:and
1809:and
1709:and
1611:The
1571:The
1561:1963
1557:1962
1527:The
1500:are
1496:and
1488:are
1484:and
1226:and
1151:and
974:The
933:and
890:and
871:and
836:and
816:, a
724:O(â)
713:Loop
532:and
2559:Zbl
2333:30
2319:29
2305:28
2291:27
2277:26
2263:25
2258:12
2252:15
2249:24
2235:23
2221:22
2207:21
2193:20
2179:19
2165:18
2151:17
2140:14
2137:16
2123:15
2109:14
2095:13
2081:12
2067:11
2053:10
1768:is
1764:If
1751:â 1
1590:An
1543:is
1511:is
1462:in
1437:of
1417:is
1359:of
1114:An
1078:= e
1045:!.
1041:is
1020:! (
988:of
828:is
812:In
639:Sp(
627:SU(
603:SO(
567:SL(
555:GL(
2658::
2644:A
2588:.
2557:.
2450:.
2342:3
2339:1
2336:4
2328:0
2325:1
2322:1
2314:2
2311:2
2308:4
2300:2
2297:3
2294:5
2286:1
2283:1
2280:2
2272:0
2269:2
2266:2
2255:3
2244:0
2241:1
2238:1
2230:1
2227:1
2224:2
2216:1
2213:1
2210:2
2202:3
2199:2
2196:5
2188:0
2185:1
2182:1
2174:3
2171:2
2168:5
2160:0
2157:1
2154:1
2146:9
2143:5
2132:0
2129:1
2126:1
2118:1
2115:1
2112:2
2104:0
2101:1
2098:1
2090:3
2087:2
2084:5
2076:0
2073:1
2070:1
2062:1
2059:1
2056:2
2048:0
2045:2
2042:2
2039:9
2034:2
2031:3
2028:5
2025:8
2020:0
2017:1
2014:1
2011:7
2006:1
2003:1
2000:2
1997:6
1992:0
1989:1
1986:1
1983:5
1978:0
1975:2
1972:2
1969:4
1964:0
1961:1
1958:1
1955:3
1950:0
1947:1
1944:1
1941:2
1936:0
1933:1
1930:1
1927:1
1922:0
1919:0
1916:0
1913:0
1883:,
1868:.
1797:=
1761:.
1734:pq
1597:A
1583:A
1563:)
1559:,
1445:.
1389:.
1371:.
1325:.
1262:,
1222:,
1173:A
1159:.
1140:.
1087:th
1074:=
960:A
937:.
906:.
840:.
615:U(
591:E(
579:O(
37:â
2626:)
2624:n
2598:.
2565:.
1898:n
1874:n
1866:n
1862:n
1858:n
1854:n
1842:n
1838:n
1831:n
1827:n
1819:b
1815:a
1811:q
1807:p
1802:q
1799:p
1795:n
1790:n
1786:n
1774:n
1766:n
1755:q
1749:p
1743:p
1739:q
1726:n
1722:n
1715:n
1703:n
1699:n
1695:n
1679:n
1668:n
1608:;
1601:;
1509:G
1498:b
1494:a
1486:q
1482:p
1478:q
1475:p
1468:G
1443:G
1439:G
1431:G
1415:G
1387:G
1365:G
1361:G
1357:H
1346:G
1284:k
1264:q
1260:n
1256:q
1252:q
1236:p
1201:k
1194:G
1187:k
1185:(
1183:G
1094:a
1084:n
1076:a
1072:a
1067:a
1062:n
1043:n
1038:n
1029:n
1022:n
1018:n
1002:n
990:n
981:n
978:S
968:4
966:S
801:e
794:t
787:v
683:8
681:E
675:7
673:E
667:6
665:E
659:4
657:F
651:2
649:G
643:)
641:n
631:)
629:n
619:)
617:n
607:)
605:n
595:)
593:n
583:)
581:n
571:)
569:n
559:)
557:n
499:)
486:Z
474:)
461:Z
437:)
424:Z
415:(
328:p
293:Q
285:n
282:D
272:n
269:A
261:n
258:S
250:n
247:Z
20:)
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