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math.GR2023
Non-trivial units of complex group rings
Giles Gardam
The Kaplansky unit conjecture for group rings is false in characteristic zero.
math.GR2023
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.GR2018
Profinite rigidity in the SnapPea census
Giles Gardam
A well-known question asks whether any two non-isometric finite volume hyperbolic 3-manifolds are distinguished from each other by the finite quotients of their fundamental groups.…