数学季刊 ›› 2006, Vol. 21 ›› Issue (3): 351-357.

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可解群的若干充分条件

  

  1. Department of Computer and Mathematics, Shanxi Teacher's University, Linfen 041004, China
  • 收稿日期:2003-02-12 出版日期:2006-09-30 发布日期:2023-11-27
  • 作者简介:WANG Li-fang(1978-),female,native of Changzhi,Shanxi,M.S.D.,engages in group theory; ZHANG Qin-hai(1955-),male,native of Yicheng,Shanxi,a professor of Shanxi Teachers University,Ph.D., engages in group theory.
  • 基金资助:
     Supported by the NSF of China(10471085) Supported by the Shanxi Province(20051007) Supported by the Returned Chinese Students Found of Shanxi Province(Jinliuguanban [2004]7);

Some Sufficient Conditions of a Solvable Group

  1. Department of Computer and Mathematics, Shanxi Teacher's University, Linfen 041004, China
  • Received:2003-02-12 Online:2006-09-30 Published:2023-11-27
  • About author:WANG Li-fang(1978-),female,native of Changzhi,Shanxi,M.S.D.,engages in group theory; ZHANG Qin-hai(1955-),male,native of Yicheng,Shanxi,a professor of Shanxi Teachers University,Ph.D., engages in group theory.
  • Supported by:
     Supported by the NSF of China(10471085) Supported by the Shanxi Province(20051007) Supported by the Returned Chinese Students Found of Shanxi Province(Jinliuguanban [2004]7);

摘要: A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.

关键词: a solvable group, a s-semipermutable subgroup, a semipermutable subgroup 

Abstract: A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.

Key words: a solvable group, a s-semipermutable subgroup, a semipermutable subgroup 

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