Effective indices of subgroups in Baumslag--Pride groups with free quotients

TL;DR

This paper provides effective bounds on the minimal index of subgroups with nonabelian free quotients in Baumslag--Pride groups with free quotients, establishing polynomial upper bounds and lower bounds based on relator length.

Contribution

It introduces explicit polynomial bounds for subgroup indices with free quotients in Baumslag--Pride groups, advancing understanding of subgroup structure in these groups.

Findings

Index bounded by polynomial in relator length

Lower bounds on subgroup index established

Effective estimates for subgroup indices provided

Abstract

Given a group with at least two more generators than relations, we give an effective estimate on the minimal index of a subgroup with a nonabelian free quotient. We show that the index is bounded by a polynomial in the length of the relator word. We also provide a lower bound on the index.