Pro-$\mathcal{C}$ groups acting on profinite trees

Lucas C. Lopes; Pavel A. Zalesskii

Pro-$\mathcal{C}$ groups acting on profinite trees

Group Theory 2026-07-26 v1

Authors: Lucas C. Lopes , Pavel A. Zalesskii

Abstract

We provide necessary conditions for pro- $\mathcal{C}$ subgroups to embed into free profinite products, where $\mathcal{C}$ 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.

Cite

@article{arxiv.2607.23875,
  title  = {Pro-$\mathcal{C}$ groups acting on profinite trees},
  author = {Lucas C. Lopes and Pavel A. Zalesskii},
  journal= {arXiv preprint arXiv:2607.23875},
  year   = {2026}
}