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arXiv · 2607.23875

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

Lucas C. Lopes·Pavel A. Zalesskii
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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.

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Lucas C. Lopes, Pavel A. Zalesskii. 2026-07-26. Pro-$\mathcal{C}$ groups acting on profinite trees. https://arxiv.org/abs/2607.23875

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