3 papers
math.GR2026
Virtual retracts in groups acting on rooted trees
Jorge Fariña-Asategui, Jon Merladet Urigüen
We study virtual retracts in groups acting on rooted trees. We show that finitely generated branch groups do not have the local retraction (LR) property. Furthermore, we specialize…
math.GR2025
Property (VRC) and virtual fibering for amalgamated free products
Jon Merladet Urigüen, Ashot Minasyan
This paper focuses on studying properties of amalgamated free products , where the amalgamated subgroup is virtually cyclic. First, we prove that if the fac…
math.GR2025
Virtual retractions in free constructions
Jon Merladet Urigüen, Ashot Minasyan
A group has property (VRC) if every cyclic subgroup is a virtual retract. This property is stable under many standard group-theoretic constructions and is enjoyed by all virtua…