247:, is a generalization of a formation, consisting of a class of groups such that a group is in the class if and only if every primitive factor group is in the class. Here a group is called primitive if it has a self-
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Schunck, Hermann (1967), "H-Untergruppen in endlichen auflösbaren
Gruppen",
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Gaschütz, Wolfgang (1962), "Zur
Theorie der endlichen auflösbaren Gruppen",
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96:, the formation of π-groups for a set of primes π, and the formation of
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and subgroups, but not necessarily extensions. The families of finite
174:{\displaystyle 1\rightarrow A\rightarrow B\rightarrow C\rightarrow 1\ }
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is a
Melnikov formation which is also closed under taking
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Ballester-Bolinches, Adolfo; Ezquerro, Luis M. (2006),
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82:Some examples of formations are the formation of
235:are almost full, but neither full nor Melnikov.
64:introduced formations to unify the theory of
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32:closed under taking images and such that if
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371:Fried, Michael D.; Jarden, Moshe (2004),
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223:is one which is closed under quotients,
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343:Doerk, Klaus; Hawkes, Trevor (1992),
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128:has the property that for every
48:are in the formation then so is
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243:A Schunck class, introduced by
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124:. Thus a Melnikov formation
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483:Mathematische Zeitschrift
404:Mathematische Zeitschrift
283:Fried & Jarden (2004)
271:Fried & Jarden (2004)
251:normal abelian subgroup.
314:Classes of finite groups
112:is closed under taking
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346:Finite soluble groups
221:almost full formation
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130:short exact sequence
496:10.1007/BF01112173
417:10.1007/BF01162386
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110:Melnikov formation
457:978-3-540-03825-2
356:978-3-11-012892-5
328:978-1-4020-4718-3
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444:Endliche Gruppen
440:Huppert, Bertram
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70:Carter subgroups
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239:Schunck classes
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30:class of groups
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18:group theory
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490:: 326–330,
411:: 300–305,
231:and finite
22:mathematics
395:1055.12003
305:References
504:0025-5874
425:0025-5874
214:subgroups
163:→
157:→
151:→
145:→
114:quotients
26:formation
522:Category
442:(1967),
512:0209356
466:0224703
433:0179257
365:1169099
337:2241927
191:are in
87:-groups
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201:is in
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89:for a
74:finite
255:Notes
91:prime
28:is a
500:ISSN
470:OCLC
452:ISBN
421:ISSN
381:ISBN
351:ISBN
323:ISBN
187:and
120:and
68:and
40:and
24:, a
492:doi
413:doi
391:Zbl
219:An
72:of
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263:^
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208:A
205:.
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494::
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203:M
199:B
193:M
189:C
185:A
166:1
160:C
154:B
148:A
142:1
126:M
94:p
85:p
58:N
56:∩
54:M
52:/
50:G
46:N
44:/
42:G
38:M
36:/
34:G
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