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M p -supplemented subgroups of finite groups

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Abstract

A subgroup K of G is M p -supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = p α. In this paper we prove the following: Let p be a prime divisor of |G| and let H be a p-nilpotent subgroup having a Sylow p-subgroup of G. Suppose that H has a subgroup D with D p ≠ 1 and |H: D| = p α. Then G is p-nilpotent if and only if every subgroup T of H with |T| = |D| is M p -supplemented in G and N G (T p )/C G (T p ) is a p-group.

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Authors and Affiliations

  1. School of Mathematical Sciences Yangzhou University, Yangzhou, People’s Republic of China

    B. Gao & L. Miao

  2. Wuxi Institute of Technology, Wuxi, People’s Republic of China

    J. Tang

Authors
  1. B. Gao
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  2. J. Tang
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  3. L. Miao
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Corresponding author

Correspondence to L. Miao.

Additional information

Yangzhou. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 1, pp. 25–32, January–February, 2016; DOI: 10.17377/smzh.2016.57.103.

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Gao, B., Tang, J. & Miao, L. M p -supplemented subgroups of finite groups. Sib Math J 57, 18–23 (2016). https://doi.org/10.1134/S0037446616010031

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  • DOI: https://doi.org/10.1134/S0037446616010031

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