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Influence of properties of maximal subgroups on the structure of a finite group

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Abstract

We establish some tests for the solvability of finite groups and describe one class of unsolvable groups. We prove that an unsolvable group G such that a maximal subgroup M= P × H is nilpotent and the 2-Sylow subgroup P of M is metacyclic has a normal series GD-g0∼TD-{1} such that T is contained in M, G0/T ∼- PSL (2, q), where q is a power of a prime of the form 2n± 1 and the index of g0 in G is not greater than 2.

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Authors and Affiliations

  1. T. G. Shevchenko Orsk Pedagogical Institute, USSR

    V. S. Monakhov

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  1. V. S. Monakhov
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 183–190, February, 1972.

The author warmly thanks V. A. Vedernikov for his guidance and assistance in completing this work.

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Monakhov, V.S. Influence of properties of maximal subgroups on the structure of a finite group. Mathematical Notes of the Academy of Sciences of the USSR 11, 115–118 (1972). https://doi.org/10.1007/BF01097928

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  • DOI: https://doi.org/10.1007/BF01097928

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