On the rank of the intersection of free subgroups in virtually free groups

TL;DR

This paper establishes new bounds on the rank of intersections of free subgroups within virtually free groups, extending classical inequalities to more general group structures.

Contribution

It introduces generalized estimates for subgroup intersections in virtually free groups and fundamental groups of graphs of groups, expanding classical results like Hanna Neumann's inequality.

Findings

Derived bounds similar to Hanna Neumann inequality for virtually free groups

Extended estimates to fundamental groups of finite graphs of groups

Provided a unified approach to subgroup intersection ranks in complex group structures

Abstract

We prove an estimate for the rank of the intersection of free subgroups in virtually free groups, which is analogous to the Hanna Neumann inequality for subgroups in a free group and to the S.V. Ivanov estimate for subgroups in free products of groups. We also prove a more general estimate for the rank of the intersection of free subgroups in the fundamental group of a finite graph of groups with finite edge groups.