6 papers
Epimorphism testing with dihedral targets
Murray Elder, Jerry Shen, Armin Weiß
We consider the problem of deciding whether or not there is an epimorphism from the class of finitely presented groups to a fixed finite group. We show this problem is $\mathsf{NP}…
Testing epimorphism onto the bicyclic monoid is -complete
Luka Carroll, Murray Elder
We prove that deciding whether there is a surjective homomorphism from an arbitrary finitely presented inverse monoid onto the bicyclic monoid is -complete. As part of…
New constructions of free products and geodetic Cayley graphs
Joshua Abraham, Murray Elder, Adam Piggott +1
A connected graph is called \emph{geodetic} if there is a unique shortest path between each pair of vertices. We introduce a systematic method for constructing new presentations of…
On the complexity of epimorphism testing with virtually abelian targets
Murray Elder, Jerry Shen, Armin Weiß
Friedl and Löh (2021, Confl. Math.) prove that testing whether or not there is an epimorphism from a finitely presented group to the direct product of an abelian and a finite group…
Finite groups with geodetic Cayley graphs
Murray Elder, Adam Piggott, Florian Stober +2
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups…
Graphs and groups with unique geodesics
Murray Elder, Giles Gardam, Adam Piggott +2
A connected graph is called \emph{geodetic} if there is a unique geodesic between each pair of vertices. In this paper we prove that if a finitely generated group admits a Cayley g…