TY - JOUR
T1 - On $\mathfrak{F}_\tau$-$s$-Supplemented Subgroups of Finite Groups
AU - Mao , Yuemei
AU - Ma , Xiaojian
JO - Journal of Mathematical Study
VL - 1
SP - 50
EP - 56
PY - 2016
DA - 2016/03
SN - 49
DO - http://doi.org/10.4208/jms.v49n1.16.06
UR - https://global-sci.org/intro/article_detail/jms/988.html
KW - Subnormal subgroup, subgroup functor, soluble group.
AB - <p style="text-align: justify;">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.</p>