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A generalized CAP-subgroup of a finite group

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Abstract

Let A be a subgroup of a finite group G. We say that A is a generalized CAP-subgroup of G if for each chief factor H/K of G either A avoids H/K or the following holds: (1) If H/K is non-abelian, then |H: (A∩H)K| is a p′-number for every p ∈ π((A∩H)K/K); (2) If H/K is a p-group, then |G: N G (K(A∩H))| is a p-number. In this paper, we use the generalized CAP-subgroup to characterize the structure of finite groups. Some new characterizations of the hypercyclically embedded subgroups of a finite group are obtained and a series of known results are generalized.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    WenBin Guo

  2. Department of Mathematics, Francisk Skorina Gomel State University, Gomel, 246019, Belarus

    Alexander N. Skiba

  3. School of Science, Jiangnan University, Wuxi, 214122, China

    NanYing Yang

Authors
  1. WenBin Guo
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  2. Alexander N. Skiba
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  3. NanYing Yang
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Correspondence to WenBin Guo.

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Guo, W., Skiba, A.N. & Yang, N. A generalized CAP-subgroup of a finite group. Sci. China Math. 58, 1–12 (2015). https://doi.org/10.1007/s11425-015-5005-5

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  • DOI: https://doi.org/10.1007/s11425-015-5005-5

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