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Zbl 0935.20013
Chen, Zhongmu
Generalization of the Schur-Zassenhaus theorem.
(English)
[J] J. Math., Wuhan Univ. 18, No.3, 290-294 (1998). ISSN 0255-7797

The main results of this paper are as follows: (1) If a Hall $\pi$-subgroup $H$ of a finite group $G$ is $S$-seminormal in $G$, then $H$ has a complement in $G$ and all such complements are conjugate in $G$. (2) If the Sylow $p$-subgroups of a finite group $G$ are $S$-seminormal in $G$, then $G$ is $p$-solvable.
[Wang Cun-Zheng (Chengdu)]
MSC 2000:
*20D20 Sylow subgroups of finite groups
20D40 Products of subgroups of finite groups
20D35 Subnormal subgroups of finite groups
20D10 Solvable finite groups

Keywords: seminormal subgroups; $\pi$-separable groups; Hall $\pi$-subgroups; finite groups; complements; Sylow subgroups; $p$-solvable groups

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