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math.GR2025
Groups with a finite Busemann boundary are virtually cyclic
Corentin Bodart, Liran Ron-George, Ariel Yadin
This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a C…
math.GR2025
Twisted commutativity and conjugacy ratio in groups
Laura Ciobanu, Gemma Crowe, Pieter Senden +1
In this paper we introduce and study the degree of twisted commutativity and the twisted conjugacy ratio of a finitely generated group . The degree of twisted commutativity $\ma…
math.GR2025
On finite extensions of lamplighter groups
Corentin Bodart
We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, provid…