4 papers
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…
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…
On the complexity of epimorphism testing with virtually abelian targets
Murray Elder, Jerry Shen, Armin WeiÃ
Friedl and Löh (2021, Confl. Math.) prove that testing whether or not there is an epimorphism from a finitely presented group to a virtually cyclic group, or to the direct product…
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…