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The influence of weakly-supplemented subgroups on the structure of finite groups

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Abstract

A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper it is proved that a finite group G is p-nilpotent provided p is the smallest prime number dividing the order of G and every minimal subgroup of P∩G′ is weakly-supplemented in N G (P), where P is a Sylow p-subgroup of G. As applications, some interesting results with weakly-supplemented minimal subgroups of P∩G′ are obtained.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China

    Qingjun Kong

  2. Department of Basic Sciences, Shandong Water Polytechnic, Rizhao, 276826, People’s Republic of China

    Qingfeng Liu

Authors
  1. Qingjun Kong
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  2. Qingfeng Liu
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Corresponding author

Correspondence to Qingjun Kong.

Additional information

The paper is dedicated to Professor John Cossey on his 70th birthday

The research of the authors is supported by the National Natural Science Foundation of China (11301378), SGRC (GZ310), the Research Grant of Tianjin Polytechnic University, and Shanghai Leading Academic Discipline Project (J50101).

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Kong, Q., Liu, Q. The influence of weakly-supplemented subgroups on the structure of finite groups. Czech Math J 64, 173–182 (2014). https://doi.org/10.1007/s10587-014-0092-y

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  • DOI: https://doi.org/10.1007/s10587-014-0092-y

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