On $\mathfrak{U}\Phi$-hypercentrally embedded subgroups of finite groups

V. A. Vasilyev

Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 66-71

Résumé

A subgroup $M$ of a group $G$ is a modular subgroup in $G$ if the following conditions are true: $\langle X, M\cap Z\rangle=\langle X, M\rangle\cap Z$ for all $X\leqslant G$, $Z\leqslant G$ with $X\leqslant Z$, and $\langle M, Y\cap Z\rangle=\langle M, Y\rangle\cap Z$ for all $Y\leqslant G$, $Z\leqslant G$ with $M\leqslant Z$. Conditions for $\mathfrak{U}\Phi$-embedding of hypercentral subgroups of finite groups with given modular primary subgroups are found.

Détail

Keywords: finite group, modular subgroup, Sylow $p$-subgroup, $\mathfrak{U}\Phi$-hypercentre.