2019
Том 71
№ 11

# On weakly s -normal subgroups of finite groups

Abstract

Assume that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is $s$-permutably imbedded in $G$ if, for every prime number p that divides $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; a subgroup $H$ is $s$-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$; a subgroup $H$ is weakly $s$-normal in $G$ if there are a subnormal subgroup $T$ of $G$ and a subgroup $H_{*}$ of $H$ such that $G = HT$ and $H \bigcap T ≤ H_{*}$, where $H_{*}$ is a subgroup of $H$ that is either $s$-permutably imbedded or $s$-semipermutable in $G$. We investigate the influence of weakly $s$-normal subgroups on the structure of finite groups. Some recent results are generalized and unified.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 11, pp 1770-1780.

Citation Example: Li Yangming, Qiao Shouhong On weakly s -normal subgroups of finite groups // Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1555-1564.

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