---
abstract: |
    In the theory of one-relator groups, Magnus subgroups, which are free subgroups obtained by omitting a generator that occurs in the given relator, play an essential structural role. In a previous article, the author proved that if two distinct Magnus subgroups $M$ and $N$ of a one-relator group, with free bases $S$ and $T$ are given, then the intersection of $M$ and $N$ is either the free subgroup $P$ generated by the intersection of $S$ and $T$ or the free product of $P$ with an infinite cyclic group.

    The main result of this article is that if $M$ and $N$ are Magnus subgroups (not necessarily distinct) of a one-relator group $G$ and $g$ and $h$ are elements of $G$, then either the intersection of $gMg^{-1}$ and $hNh^{-1}$ is cyclic (and possibly trivial), or $gh^{-1}$ is an element of $NM$ in which case the intersection is a conjugate of the intersection of $M$ and $N$.
address: |
    School of Mathematical Sciences\
    Queen Mary, University of London\
    Mile End Road\
    London E1 4NS\
    UK
author:
- Donald J Collins
bibliography:
- 'link.bib'
title: |
    Intersections of conjugates of Magnus subgroups\
    of one-relator groups
---

In the theory of one-relator 