On s¤-Completions of Maximal Subgroups of Finite Groups

GAO Hui, GAO Sheng-zhe, YIN Li

doi:10.13371/j.cnki.chin.q.j.m.2015.03.009

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 3: 381 - 388

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.03.009

On s^¤-Completions of Maximal Subgroups of Finite Groups

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School of Science, Dalian Ocean University

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.

Received date: 2014-03-28

Online published: 2020-11-20

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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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GAO Hui, GAO Sheng-zhe, YIN Li . On s^¤-Completions of Maximal Subgroups of Finite Groups[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(3) : 381 -388 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.009

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