arXiv subjects

I. L. Sokhor

Publications and source records attributed to I. L. Sokhor.

3 recordsLinked to original sources

arXiv2021

Finite groups with $\mathbb{P}$-subnormal and strongly permutable subgroups

Let $H$ be a subgroup of a group $G$. The permutizer $P_G(H)$ is the subgroup generated by all cyclic subgroups of $G$ which permute with $H$. A subgroup $H$ of a group $G$ is strongly permutable in $G$ if $P_U(H)=U$ for every subgroup $U$ of $G$ such that~$H\le U\le G$. We investigate groups with $\mathbb{P}$-subnormal or strongly permutable Sylow and primary cyclic subgroups. In particular, we prove that groups with all strongly permutable primary cyclic subgroups are supersoluble.

math.GR↗

arXiv2019

On grouops with formational subnormal or self-normalizing subgroups

We establish the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups in case $\mathfrak{F}$ is a subgroup-closed saturated superradical formation containing all nilpotent groups.

math.GR↗

arXiv2016

Finite soluble groups with nilpotent wide subgroups

A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent wide subgroups has the quotient group by its hypercenter with no wide subgroups.

math.GR↗