# On one question of Shemetkov about composition formations

## TL;DR

This paper introduces a new construction of composition formations encompassing various classes of groups and provides partial answers to a question about the intersection of maximal subgroups and hypercenters within these formations.

## Contribution

It presents a novel construction of composition formations that includes several known classes and addresses Shemetkov's question regarding subgroup intersections.

## Key findings

- Introduced a new construction of composition formations.
- Provided partial answers to Shemetkov's question.
- Included formations of quasinilpotent, $c$-supersoluble groups, and others.

## Abstract

In this paper one construction of composition formations was introduced. This construction contains formations of quasinilpotent groups, $c$-supersoluble groups, groups defined by ranks of chief factors and some new classes of groups. A partial answer on a question of L.\,A. Shemetkov about the intersection of $\mathfrak{F}$-maximal subgroups and the $\mathfrak{F}$-hypercenter was given for these composition formations.