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Finite groups with generalized subnormal embedding of Sylow subgroups

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Abstract

Given a set π of primes and a hereditary saturated formation F, we study the properties of the class of groups G for which the identity subgroup and all Sylow p-subgroups are F-subnormal (K-F-subnormal) in G for each p in π. We show that such a class is a hereditary saturated formation and find its maximal inner local screen. Some criteria are obtained for the membership of a group in a hereditary saturated formation in terms of its formation subnormal Sylow subgroups.

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Authors and Affiliations

  1. Francisk Skorina Gomel State University, Gomel, Belarus

    A. F. Vasil’ev & A. S. Vegera

  2. Belarusian State University of Transport, Gomel, Belarus

    T. I. Vasil’eva

Authors
  1. A. F. Vasil’ev
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  2. T. I. Vasil’eva
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  3. A. S. Vegera
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Corresponding author

Correspondence to A. F. Vasil’ev.

Additional information

Gomel. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 2, pp. 259–275, March–April, 2016; DOI: 10.17377/smzh.2016.57.203.

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Vasil’ev, A.F., Vasil’eva, T.I. & Vegera, A.S. Finite groups with generalized subnormal embedding of Sylow subgroups. Sib Math J 57, 200–212 (2016). https://doi.org/10.1134/S0037446616020038

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  • DOI: https://doi.org/10.1134/S0037446616020038

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