2 citations · 2 across the 5 of their papers we have counts for
5 papers · 1 filter
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…
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…
On -geodetic graphs and groups
Murray Elder, Adam Piggott, Kane Townsend
We call a graph -geodetic, for some , if it is connected and between any two vertices there are at most geodesics. It is shown that any hyperbolic group with a -…
Normalizers of Sylow subgroups in finite reflection groups
Kane Douglas Townsend
Let be a finite reflection group, either real or complex, and a Sylow -subgroup of . We prove the existence of a semidirect product decomposition of $N_W(S_\e…
Classification of Sylow classes of parabolic and reflection subgroups in unitary reflection groups
Kane Douglas Townsend
Let be a prime divisor of the order of a finite unitary reflection group. We classify up to conjugacy the parabolic and reflection subgroups that are minimal with respect to…