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Absolutely simple group

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212: 100: 120: 74: 54: 253: 129:. However, in the infinite case, absolutely simple is a stronger property than simple. The property of being strictly simple is somewhere in between. 182: 246: 211: 272: 277: 239: 169:, Graduate Texts in Mathematics, vol. 80 (Second ed.), New York: Springer-Verlag, p. 381, 143: 25: 138: 178: 164: 170: 192: 79: 188: 33: 223: 105: 59: 39: 266: 219: 126: 21: 17: 174: 125:
In the finite case, a group is absolutely simple if and only if it is
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is an absolutely simple group if the only serial subgroups of
227: 108: 82: 62: 42: 114: 94: 68: 48: 247: 8: 89: 83: 254: 240: 107: 81: 61: 41: 155: 7: 208: 206: 14: 210: 166:A course in the theory of groups 32:if it has no proper nontrivial 163:Robinson, Derek J. S. (1996), 1: 226:. You can help Knowledge by 102:(the trivial subgroup), and 294: 205: 122:itself (the whole group). 175:10.1007/978-1-4419-8594-1 222:-related article is a 116: 96: 70: 50: 144:Strictly simple group 117: 97: 95:{\displaystyle \{e\}} 71: 51: 273:Properties of groups 106: 80: 60: 40: 278:Group theory stubs 139:Ascendant subgroup 112: 92: 66: 46: 20:, in the field of 235: 234: 115:{\displaystyle G} 69:{\displaystyle G} 49:{\displaystyle G} 30:absolutely simple 285: 256: 249: 242: 214: 207: 197: 195: 160: 121: 119: 118: 113: 101: 99: 98: 93: 75: 73: 72: 67: 55: 53: 52: 47: 34:serial subgroups 293: 292: 288: 287: 286: 284: 283: 282: 263: 262: 261: 260: 203: 201: 200: 185: 162: 161: 157: 152: 135: 104: 103: 78: 77: 58: 57: 38: 37: 12: 11: 5: 291: 289: 281: 280: 275: 265: 264: 259: 258: 251: 244: 236: 233: 232: 215: 199: 198: 183: 154: 153: 151: 148: 147: 146: 141: 134: 131: 111: 91: 88: 85: 65: 45: 28:is said to be 13: 10: 9: 6: 4: 3: 2: 290: 279: 276: 274: 271: 270: 268: 257: 252: 250: 245: 243: 238: 237: 231: 229: 225: 221: 216: 213: 209: 204: 194: 190: 186: 184:0-387-94461-3 180: 176: 172: 168: 167: 159: 156: 149: 145: 142: 140: 137: 136: 132: 130: 128: 123: 109: 86: 63: 43: 35: 31: 27: 23: 19: 228:expanding it 220:group theory 217: 202: 165: 158: 124: 29: 22:group theory 15: 36:. That is, 18:mathematics 267:Categories 150:References 133:See also 193:1357169 191:  181:  127:simple 218:This 26:group 224:stub 179:ISBN 76:are 24:, a 171:doi 16:In 269:: 189:MR 187:, 177:, 255:e 248:t 241:v 230:. 196:. 173:: 110:G 90:} 87:e 84:{ 64:G 44:G

Index

mathematics
group theory
group
serial subgroups
simple
Ascendant subgroup
Strictly simple group
A course in the theory of groups
doi
10.1007/978-1-4419-8594-1
ISBN
0-387-94461-3
MR
1357169
Stub icon
group theory
stub
expanding it
v
t
e
Categories
Properties of groups
Group theory stubs

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