On free decompositions of verbally closed subgroups of free products of finite groups

TL;DR

This paper investigates the conditions under which subgroups of free products of finite groups are verbally closed, focusing on their Kurosh decomposition to establish necessary criteria.

Contribution

It provides necessary conditions based on Kurosh decomposition for subgroups to be verbally closed in free products of finite groups.

Findings

Identifies necessary conditions for verbal closure

Links Kurosh decomposition to subgroup properties

Advances understanding of subgroup structure in free products

Abstract

For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.