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math.GR2025
Unimodular random graphs with Property (T) have cost one
Łukasz Grabowski, Héctor Jardón-Sánchez, Sam Mellick
Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem,…
math.GR2023
On group rings of virtually abelian groups
Joan Claramunt, Lukasz Grabowski
Let be a finitely generated torsion-free group. We show that the statement of being virtually abelian is equivalent to the statement that the -regular closure of the gro…