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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 6, Pages 1238–1249
(Mi smj1915)
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This article is cited in 1 scientific paper (total in 1 paper)
Formations generated by a group of socle length 2
V. P. Burichenko Institute of Mathematics, National Academy of Sciences of the Republic of Belarus
Abstract:
Gaschütz conjectured that a formation generated by a finite group contains only finitely many subformations. In the present article we prove this conjecture for the groups of socle length at most 2. (We say that a group has socle length 1 if it coincides with its socle and has socle length 2 if its quotient by the socle has socle length 1.) Earlier Gaschütz's conjecture was proven in several particular cases including all soluble groups.
Keywords:
finite groups, formation.
Received: 11.07.2007
Citation:
V. P. Burichenko, “Formations generated by a group of socle length 2”, Sibirsk. Mat. Zh., 49:6 (2008), 1238–1249; Siberian Math. J., 49:6 (2008), 988–996
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https://www.mathnet.ru/eng/smj1915 https://www.mathnet.ru/eng/smj/v49/i6/p1238
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Abstract page: | 233 | Full-text PDF : | 84 | References: | 53 |
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