Burnside Condition on Some Intersection Subgroups

TL;DR

This paper proves that the intersection of subgroups with the Burnside condition in free groups also satisfies the Burnside condition, using graph-theoretic methods introduced by Stallings.

Contribution

It introduces a new proof of the Burnside condition for subgroup intersections in free groups utilizing graph theory.

Findings

Burnside condition preserved under subgroup intersection

Graph-theoretic approach effective for subgroup properties

Extends understanding of Burnside groups in free groups

Abstract

In this paper, using the notions graphs, core graphs, immersions and covering maps of graphs, introduced by Stallings in 1983, we prove the Burnside condition for the intersection of subgroups of free groups with Burnside condition.