A complete classification of minimal non-PS-groups

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• 作者：PENGFEI GUO (1) (2)
  JUNXIN WANG (3)
  HAILIANG ZHANG (4)
  
  1. School of Mathematics and Information Engineering ; Lianyungang Normal College ; Lianyungang ; 222006 ; People鈥檚 Republic of China
  2. Department of Civil and Architectural Engineering ; City University of Hong Kong ; Hong Kong ; 999077 ; People鈥檚 Republic of China
  3. Department of Mathematics ; Shanxi University of Finance and Economics ; Taiyuan ; 030006 ; People鈥檚 Republic of China
  4. Department of Mathematics ; Zhejiang Ocean University ; Zhoushan ; 316000 ; People鈥檚 Republic of China
  
• 关键词：PS ; groups ; minimal non ; PS ; groups ; supersolvable groups ; power automorphisms. ; 20D10 ; 20E34.
• 刊名：Proceedings Mathematical Sciences
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：124
• 期：4
• 页码：511-516
• 全文大小：168 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer India
• ISSN：0973-7685

文摘

Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.