66 citations · 122 across the 22 of their papers we have counts for
24 papers
Generalising Collins' Theorem
James Howie, Hamish Short
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.
On singular equations over torsion-free groups
Martin Edjvet, James Howie
We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-fr…
Coherence and one-relator products of locally indicable groups
James Howie, Hamish Short
We extend several results of Helfer, Wise, Louder and Wilton related to coherence in one-relator groups to the more general setting of one-relator products of locally indicable gro…
Planar Whitehead graphs with cyclic symmetry arising from the study of Dunwoody manifolds
James Howie, Gerald Williams
A fundamental theorem in the study of Dunwoody manifolds is a classification of finite graphs on vertices that satisfy seven conditions (concerning planarity, regularity, and…
Generalised triangle groups of type (2,3,2) with no cyclic essential representations
James Howie, Olexandr Konovalov
A conjecture of Roseberger asserts that every generalised triangle group either is virtually soluble or contains a non-abelian free subgroup. Modulo two exceptional cases, we verif…
Fibonacci type presentations and 3-manifolds
James Howie, Gerald Williams
We study the cyclic presentations with relators of the form and the groups they define. These "groups of Fibonacci type" were introduced by Johnson and Maw…