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math.GR2025
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…
math.GR2024
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…
math.GR2024
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…