Algorithmic Problems in Amalgams of Finite Groups: Conjugacy and Intersection Properties

TL;DR

This paper extends Stallings' geometric methods to address algorithmic problems related to finitely generated subgroups within amalgams of finite groups, advancing computational group theory techniques.

Contribution

It develops generalized Stallings' methods to solve decision problems for subgroups in amalgams of finite groups, a novel extension of existing geometric approaches.

Findings

Successfully applied generalized Stallings' methods to algorithmic problems

Solved conjugacy and intersection decision problems in amalgams of finite groups

Enhanced understanding of subgroup properties in complex group structures

Abstract

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups. In the present paper we employ the generalized Stallings' methods, developed by the author, to solve various algorithmic problems concerning finitely generated subgroups of amalgams of finite groups.