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On the heritability of the property D π by subgroups

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Abstract

Given a set of primes π, a subgroup H of a finite group G is called a π-Hall subgroup if all prime divisors of |H| are in π while |G: H| has no prime divisors from π. A group G is said to satisfy D π -property if it possesses only one class of conjugate maximal π-subgroups or, equivalently, if the complete analog of Sylow’s theorem for Hall π-subgroups holds in G. We investigate which subgroups of D π -groups inherit the D π -property.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    E. P. Vdovin & D. O. Revin

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk-90, 630090, Russia

    N. Ch. Manzaeva

Authors
  1. E. P. Vdovin
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  2. N. Ch. Manzaeva
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  3. D. O. Revin
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Correspondence to E. P. Vdovin.

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Original Russian Text © E.P. Vdovin, N.Ch.Manzaeva, D.O. Revin, 2011, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Vol. 17, No. 4.

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Vdovin, E.P., Manzaeva, N.C. & Revin, D.O. On the heritability of the property D π by subgroups. Proc. Steklov Inst. Math. 279 (Suppl 1), 130–138 (2012). https://doi.org/10.1134/S0081543812090106

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  • DOI: https://doi.org/10.1134/S0081543812090106

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