Pro-C groups acting on profinite trees

2026/07/26 by Lucas C. Lopes, Pavel A. Zalesskii
#math.GR

paper · pdf

Abstract

We provide necessary conditions for pro-C subgroups to embed into free profinite products, where C is a variety of finite groups that does not contain all finite groups. Under suitable hypotheses, we extend this result to profinite groups acting k-acylindrically on profinite trees. Finally, we show that these results can be applied to important classes of profinite groups.

Citations

• L²-Betti numbers of Dehn fillings
• Prosoluble subgroups of the profinite completion of the fundamental group of compact 3-manifolds
• Relative extensions and cohomology of profinite groups
• Right-angled Artin pro-p groups
• Negative curvature in graph braid groups
• Hierarchies for Relatively Hyperbolic Virtually Special Groups
• Virtual retraction properties in groups
• Determining Fuchsian groups by their finite quotients

Related

• Profinite Completion of Free Pro-C Groups
• Algebraic properties of profinite groups
• Homotopy of profinite groups
• Profinite groups in which centralizers are virtually procyclic
• Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation