Year: 2016
Author: Yuemei Mao, Xiaojian Ma
Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 50–56
Abstract
Let $\mathfrak{F}$ be a non-empty formation of groups, $\tau$ a subgroup functor and $H$ a $p$-subgroup of a finite group $G.$ Let $\overline{G}=G/H_G$ and $\overline{H} =H/H_G.$ We say that $H$ is $\mathfrak{F}_\tau$-$s$-supplemented in $G$ if for some subgroup $\overline{T}$ and some $\tau$-subgroup $\overline{S}$ of $\overline{G}$ contained in $\overline{H},$ $\overline{H}\overline{T}$ is subnormal in $\overline{G}$ and $\overline{H} ∩ \overline{T} ≤ \overline{S}Z_{\mathfrak{F}}(\overline{G}).$ In this paper, we investigate the influence of $\mathfrak{F}_\tau$-$s$-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n1.16.06
Journal of Mathematical Study, Vol. 49 (2016), Iss. 1 : pp. 50–56
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 7
Keywords: Subnormal subgroup subgroup functor soluble group.