TY - JOUR
AU - V. S. Monakhov
AU - M. N. Konovalova
PY - 2021/01/22
Y2 - 2022/08/09
TI - On groups with formational subnormal strictly 2-maximal subgroups
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 73
IS - 1
SE - Research articles
DO - 10.37863/umzh.v73i1.1115
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1115
AB - UDC 512.542Let $H$ be a subgroup of a finite group $G.$ If $G$ contains a maximal subgroup $M$ such that $H$ is a maximal subgroup in $M,$ then $H$ is called a $2$-maximal subgroup of $G.$ A subgroup $U$ of $G$ is said to be a strictly $2$-maximal subgroup in $G$ if $U$ is a $2$-maximal subgroup of $G$ and $U$ is not a 2-maximal subgroup in any proper subgroup of $G.$ We investigate the finite groups with $\mathfrak X$-subnormal strictly $2$-maximal subgroups for arbitrary subgroup-closed formation $\mathfrak X.$ In such a group, any proper subgroup has a nilpotent $\mathfrak X$-residual.We study in more detail the case where $\mathfrak X= \mathfrak A_1\mathfrak F$ for a subgroup-closed formation $\mathfrak F$ and the case where $\mathfrak X$ is a soluble saturated formation.
ER -