# Monakhov V. S.

### On the solvability of a finite group with $S$-seminormal Schmidt subgroups

Knyagina V. N., Monakhov V. S., Zubei E. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1511-1518

A finite nonnilpotent group is called a Schmidt group if all its proper subgroups are nilpotent. A subgroup $A$ is called $S$-seminormal (or $SS$-permutable) in a finite group $G$ if there is a subgroup B such that $G = AB$ and $A$ is permutable with every Sylow subgroup of B. We establish the criteria of solvability and $\pi$ -solvability of finite groups in which some Schmidt subgroups are $S$-seminormal. In particular, we prove the solvability of a finite group in which all supersoluble Schmidt subgroups of even order are $S$-seminormal.

### Finitely solvable groups with nilpotent wide subgroups

Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 957-962

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.

### On the Derived Length of a Finite Group with Complemented Subgroups of Order $p^2$

Knyagina V. N., Monakhov V. S.

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 874–881

It is shown that a finite group with complemented subgroups of order $p^2$ is soluble for all $p$ and its derived length does not exceed 4.

### On Solvable Normal Subgroups of Finite Groups

Gribovskaya E. E., Monakhov V. S., Sel’kin V. M.

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 950-960

We consider solvable invariant subgroups of a finite group with bounded primary indices of maximal subgroups. We establish that an invariant subgroup of this type belongs to the product of classical formations and investigate its dispersibility.