Generalized Stallings' decomposition theorem for pro-$p$ groups

Mattheus Aguiar; Pavel Zalesski

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arXiv · 2110.04601

Generalized Stallings' decomposition theorem for pro-$p$ groups

Mattheus Aguiar·Pavel Zalesski

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Abstract

The celebrated Stallings' decomposition theorem states that the splitting of a finite index subgroup $H$ of a finitely generated group $G$ as an amalgamated free product or an HNN-extension over a finite group implies the same for $G$. We generalize the pro-$p$ version of it proved by Weigel and the second author to splittings over infinite pro-$p$ groups. This generalization does not have any abstract analogs. We also prove that generalized accessibility of finitely generated pro-$p$ groups is closed for commensurability.

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BibTeX RIS

Mattheus Aguiar, Pavel Zalesski. 2021-10-09. Generalized Stallings' decomposition theorem for pro-$p$ groups. https://arxiv.org/abs/2110.04601

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