M p -supplemented subgroups of finite groups

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• 作者：B. Gao ; J. Tang ; L. Miao
• 关键词：p ; nilpotent group ; composition factor ; M p ; supplemented group ; finite group
• 刊名：Siberian Mathematical Journal
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：57
• 期：1
• 页码：18-23
• 全文大小：207 KB
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• 作者单位：B. Gao (1)
  J. Tang (2)
  L. Miao (1)
  
  1. School of Mathematical Sciences Yangzhou University, Yangzhou, People’s Republic of China
  2. Wuxi Institute of Technology, Wuxi, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260

文摘

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.