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On c#-normal subgroups infinite groups

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Abstract

A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G: In this paper, we investigate the influence of fewer c#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.

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Acknowledgements

The authors would like to thank the referees for their helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 11361006) and SRF of Guangxi University (No. XGZ130761).

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Authors and Affiliations

  1. College of Mathematics and Information Sciences, Guangxi University, Nanning, 530004, China

    Huaquan Wei, Qiao Dai, Hualian Zhang & Yubo Lv

  2. School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, 530023, China

    Liying Yang

Authors
  1. Huaquan Wei
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  2. Qiao Dai
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  3. Hualian Zhang
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  4. Yubo Lv
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  5. Liying Yang
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Correspondence to Huaquan Wei or Liying Yang.

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Wei, H., Dai, Q., Zhang, H. et al. On c#-normal subgroups infinite groups. Front. Math. China 13, 1169–1178 (2018). https://doi.org/10.1007/s11464-018-0724-x

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  • DOI: https://doi.org/10.1007/s11464-018-0724-x

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