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Finite groups with C-quasinormal subgroups

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Abstract

Consider some finite group G and a finite subgroup H of G. Say that H is c-quasinormal in G if G has a quasinormal subgroup T such that HT = G and T ∩ H is quasinormal in G. Given a noncyclic Sylow subgroup P of G, we fix some subgroup D such that 1 < |D| < | P| and study the structure of G under the assumption that all subgroups H of P of the same order as D, having no supersolvable supplement in G, are c-quasinormal in G.

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Authors and Affiliations

  1. F. Scorina Gomel State University, Gomel’, Belarus

    A. N. Skiba

  2. Belorussian State University of Transport, Gomel’, Belarus

    O. V. Titov

Authors
  1. A. N. Skiba
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  2. O. V. Titov
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Original Russian Text Copyright © 2007 Skiba A. N. and Titov O. V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 674–688, May–June, 2007.

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Skiba, A.N., Titov, O.V. Finite groups with C-quasinormal subgroups. Sib Math J 48, 544–554 (2007). https://doi.org/10.1007/s11202-007-0056-7

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  • DOI: https://doi.org/10.1007/s11202-007-0056-7

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