Generalized Stallings' decomposition theorem for pro-p groups

2021/10/09 by Mattheus Aguiar, Aguiar, Mattheus, Pavel Zalesski +1
Mathematics · #20E08 #20E18 #20E34 #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2110.04601

openalex publication_date 2021/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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