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On Π-property of some maximal subgroups of Sylow subgroups of finite groups

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Abstract

Let H be a subgroup of a finite group G. We say that H satisfies the Π-property in G if for any chief factor L/K of G, ∣G/K: NG/K(HK/K ∩ L/K)∣ is a π(HK/K∩L/K)-number. We study the influence of some p-subgroups of G satisfying the Π-property on the structure of G, and generalize some known results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Tiansheng Rd, Beibei, Chongqing, 400715, P. R. China

    Zhengtian Qiu, Jianjun Liu & Guiyun Chen

Authors
  1. Zhengtian Qiu
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  2. Jianjun Liu
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  3. Guiyun Chen
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Corresponding author

Correspondence to Guiyun Chen.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 12071376, 11971391), the Fundamental Research Funds for the Central Universities (No. XDJK2020B052), the Natural Science Foundation Project of CQ (No. cstc2021jcyjmsxmX0426) and the Fundamental Research Funds for the Central Universities (Nos. XDJK2019C116 and XDJK2019B030).

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Qiu, Z., Liu, J. & Chen, G. On Π-property of some maximal subgroups of Sylow subgroups of finite groups. Czech Math J 73, 1349–1358 (2023). https://doi.org/10.21136/CMJ.2023.0089-23

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  • DOI: https://doi.org/10.21136/CMJ.2023.0089-23

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