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Formations generated by a group of socle length 2

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Gomel’, Belarus

    V. P. Burichenko

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  1. V. P. Burichenko
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Correspondence to V. P. Burichenko.

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Original Russian Text Copyright © 2008 Burichenko V. P.

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Gomel’. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1238–1249, November–December, 2008.

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Burichenko, V.P. Formations generated by a group of socle length 2. Sib Math J 49, 988–996 (2008). https://doi.org/10.1007/s11202-008-0095-8

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  • DOI: https://doi.org/10.1007/s11202-008-0095-8

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