数学季刊 ›› 2015, Vol. 30 ›› Issue (3): 381-388.doi: 10.13371/j.cnki.chin.q.j.m.2015.03.009

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关于有限群的极大子群的s*-完备

  

  1. School of Science, Dalian Ocean University
  • 收稿日期:2014-03-28 出版日期:2015-09-30 发布日期:2020-11-20
  • 作者简介:GAO Hui(1978-), female, native of Zhuanghe, Liaoning, a lecturer of Dalian Ocean University, M.S.D., engages in finite group; GAO Sheng-zhe(Corresponding author)(1974-), male, native of Daxinganling, Heilongjiang, an associate professor of Dalian Ocean University, M.S.D., engages in finite group; YIN Li(1981-), female, native of Zhuanghe, Liaoning, a lecturer of Dalian Ocean University, M.S.D., engages in finite group.

On s¤-Completions of Maximal Subgroups of Finite Groups

  1. School of Science, Dalian Ocean University
  • Received:2014-03-28 Online:2015-09-30 Published:2020-11-20
  • About author:GAO Hui(1978-), female, native of Zhuanghe, Liaoning, a lecturer of Dalian Ocean University, M.S.D., engages in finite group; GAO Sheng-zhe(Corresponding author)(1974-), male, native of Daxinganling, Heilongjiang, an associate professor of Dalian Ocean University, M.S.D., engages in finite group; YIN Li(1981-), female, native of Zhuanghe, Liaoning, a lecturer of Dalian Ocean University, M.S.D., engages in finite group.

摘要: Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable. 

关键词: maximal subgroups, θ*-completions, s¤-completions, solvable groups, supersolvable groups

Abstract: Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable. 

Key words: maximal subgroups; θ*-completions, s¤-completions, solvable groups, supersolvable groups

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