Reading Off Kurosh Decompositions

TL;DR

This paper introduces a generalized Stallings' folding method to efficiently compute the Kurosh decomposition of subgroups within free products of finite groups, enhancing the analysis of subgroup structures.

Contribution

It presents a novel procedure that reads off Kurosh decompositions directly from subgroup graphs using an extended Stallings' folding technique.

Findings

Enables direct extraction of Kurosh decompositions from subgroup graphs

Generalizes Stallings' folding method for free products of finite groups

Improves computational approaches to subgroup structure analysis

Abstract

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used by many authors to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ our generalized Stallings' folding method to introduce a procedure, which given a subgroup H of a free product of finite groups reads off its Kurosh decomposition from the subgroup graph of H.