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A note on S-semipermutable and S-permutably embedded subgroups of finite groups

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Abstract

In this note, we obtain some criteria for p-supersolvability and p-nilpotency of a finite group and extend some known results concerning S-semipermutable and S-permutably embedded subgroups. In particular, we generalize some main results of Shen et al. (J Group Theory 13(2):257–265, 2010) and Kong and Guo (Ric Mat 68(2):571–579, 2019).

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Acknowledgements

The authors are grateful to the referee who provided his/her valuable suggestions. Haoran Yu is supported by National Natural Science Foundation of China (Grant No. 12001225 and 12171194), and the Science and Technology Department Project of Jilin Province (Grant No. 20210508024RQ). Xiaowei Xu is supported by National Natural Science Foundation of China (Grant No. 11971289). Guanghao Zhang is supported by the Doctoral Starting up Foundation of Northeast Electric Power University (Grant No. BSJXM–2021120).

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, China

    Haoran Yu & Xiaowei Xu

  2. School of Science, Northeast Electric Power University, Jilin, 132012, China

    Guanghao Zhang

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  1. Haoran Yu
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  2. Xiaowei Xu
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  3. Guanghao Zhang
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Correspondence to Guanghao Zhang.

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Yu, H., Xu, X. & Zhang, G. A note on S-semipermutable and S-permutably embedded subgroups of finite groups. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00717-1

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