2018
Том 70
№ 8

# Finitely solvable groups with nilpotent wide subgroups

Abstract

A subgroup $H$ of a finite group $G$ is called wide if each prime divisor of the order of $G$ divides the order of $H$. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to the hypercenter without wide subgroups.

Citation Example: Monakhov V. S., Sokhor I. L. Finitely solvable groups with nilpotent wide subgroups // Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 957-962.