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Some finite nonsolvable groups characterized by their solvable subgroups

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Abstract

LetG be a finite nonsolvable group andH a proper subgroup ofG. In this paper we determine the structure ofG ifG satisfies one of the following conditions:

  1. (1)

    Every solvable subgroupK(K⊉H) is eitherp-decomposable or a Schmidt group,p being the smallest odd prime factor of |G|.

  2. (2)

    |G∶H| is divisible by an odd prime and every solvable subgroupK(K⊉H) is either 2′-closed or a Schmidt group.

  3. (3)

    |G∶H| is even and every solvable subgroupK(K⊉H) is either 2-closed or a Schmidt group.

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Authors and Affiliations

  1. Department of Mathematics, Guangxi University, Guangxi, China

    Li Shirong & Zhao Yaoqing

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  1. Li Shirong
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  2. Zhao Yaoqing
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Shirong, L., Yaoqing, Z. Some finite nonsolvable groups characterized by their solvable subgroups. Acta Mathematica Sinica 4, 5–13 (1988). https://doi.org/10.1007/BF02560307

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  • DOI: https://doi.org/10.1007/BF02560307

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