Rendiconti del Seminario Matematico della Università di Padova


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Volume 126, 2011, pp. 73–88
DOI: 10.4171/RSMUP/126-5

Finite Groups with Weakly $s$-Semipermutable Subgroups

Changwen Li[1]

(1) School of Mathematical Sciences, Xuzhou Normal University, 221116, Xuzhou, China

Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-semipermutable in $G$ if $HG_{p} = G_{p}H$ for any Sylow $p$-subgroup $G_{p}$ of $G$ with $(p, |H|)=1$; $H$ is called weakly $s$-semipermutable in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T$ is $s$-semipermutable in $G$. We investigate the influence of weakly $s$-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.

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Li Changwen: Finite Groups with Weakly $s$-Semipermutable Subgroups. Rend. Sem. Mat. Univ. Padova 126 (2011), 73-88. doi: 10.4171/RSMUP/126-5