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On CAS-subgroups of finite groups

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Abstract

We introduce a new subgroup embedding property of a finite group called CAS-subgroup. Using this subgroup property, we determine the structure of finite groups with some CAS-subgroups of Sylow subgroups. Our results unify and generalize some recent theorems on solvability, p-nilpotency and supersolvability of finite groups.

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Guangzhou, 510275, China

    Huaquan Wei & Yanming Wang

  2. Department of Mathematics, Guangxi Teacher’s College, Nanning, 530001, China

    Huaquan Wei

  3. Lingnan College, Guangzhou, 510275, China

    Yanming Wang

  4. Department of Mathematics, Nanchang University, Nachang, 330047, China

    Yanming Wang

Authors
  1. Huaquan Wei
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  2. Yanming Wang
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Additional information

The authors are supported by NSF of China (10571181) and NSF of Guangxi (0447038).

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Wei, H., Wang, Y. On CAS-subgroups of finite groups. Isr. J. Math. 159, 175–188 (2007). https://doi.org/10.1007/s11856-007-0041-7

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  • DOI: https://doi.org/10.1007/s11856-007-0041-7

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