Czechoslovak Mathematical Journal, first online, pp. 1-5


On weakly-supplemented subgroups and the solvability of finite groups

Qiang Zhou

Received June 16, 2017.   Published online April 13, 2018.

Abstract:  A subgroup $H$ of a finite group $G$ is weakly-supplemented in $G$ if there exists a proper subgroup $K$ of $G$ such that $G=HK$. In this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of $G$ are obtained.
Keywords:  weakly-supplemented subgroup; complemented subgroup; solvable group
Classification MSC:  20D10, 20D20
DOI:  10.21136/CMJ.2018.0301-17

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References:
[1] Z. Arad, M. B. Ward: New criteria for the solvability of finite groups. J. Algebra 77 (1982), 234-246. DOI 10.1016/0021-8693(82)90288-5 | MR 0665175 | Zbl 0486.20018
[2] K. Doerk, T. Hawkes: Finite Soluble Groups. De Gruyter Expositions in Mathematics 4, de Gruyter, Berlin (1992). DOI 10.1515/9783110870138 | MR 1169099 | Zbl 0753.20001
[3] R. M. Guralnick: Subgroups of prime power index in a simple group. J. Algebra 81 (1983), 304-311. DOI 10.1016/0021-8693(83)90190-4 | MR 0700286 | Zbl 0515.20011
[4] P. Hall: A characteristic property of soluble groups. J. Lond. Math. Soc. 12 (1937), 198-200. DOI 10.1112/jlms/s1-12.2.198 | MR 1575073 | Zbl 0016.39204
[5] P. Hall: Complemented groups. J. London Math. Soc. 12 (1937), 201-204. DOI 10.1112/jlms/s1-12.2.201 | MR 1575074 | Zbl 0016.39301
[6] B. Huppert: Endliche Gruppen I. Springer, Berlin (1967). (In German.) DOI 10.1007/978-3-642-64981-3 | MR 0224703 | Zbl 0217.07201
[7] Q. Kong, Q. Liu: The influence of weakly-supplemented subgroups on the structure of finite groups. Czech. Math. J. 64 (2014), 173-182. DOI 10.1007/s10587-014-0092-y | MR 3247453 | Zbl 1321.20021

Affiliations:   Qiang Zhou, School of Automation, Southeast University, Nanjing 210096, P. R. China and College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China, e-mail: zq5240_2008@163.com


 
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