Generalising Collins' Theorem

TL;DR

This paper extends Collins' theorem on intersections of conjugates of Magnus subgroups from one-relator groups to one-relator products of locally indicable groups, broadening its applicability.

Contribution

It introduces a generalized theorem that applies to a wider class of groups, specifically one-relator products of locally indicable groups, expanding the scope of Collins' original result.

Findings

Generalization of Collins' theorem to new group classes

Broader applicability in group theory contexts

Potential implications for understanding subgroup intersections

Abstract

We generalise a result of D. J. Collins on intersections of conjugates of Magnus subgroups of one-relator groups to the context of one-relator products of locally indicable groups.