@article{Monakhov_Konovalova_2021, title={On groups with formational subnormal strictly 2-maximal subgroups}, volume={73}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1115}, DOI={10.37863/umzh.v73i1.1115}, abstractNote={<p>UDC 512.542</p> <p>Let $H$ be a subgroup of a finite group $G.$ <br>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 $G.$ <br>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 $G.$ <br>We investigate the finite groups with $\mathfrak X$-subnormal strictly $2$-maximal subgroups for arbitrary subgroup-closed formation $\mathfrak X.$ <br>In such a group, any proper subgroup has a nilpotent $\mathfrak X$-residual.<br>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.</p> <p> </p>}, number={1}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Monakhov, V. S. and Konovalova , M. N.}, year={2021}, month={Jan.}, pages={107 - 116} }