The profinite completion of the fundamental group of infinite graphs of groups

Mattheus, Aguiar,; Zalesski, Pavel

doi:10.48550/arxiv.2010.12720

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Fundamental Pro-p Group Of a Profinite Graph Of Pro-p Groups1

Standard Pro-p Tree1

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2021

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Cited by 1 publication

(2 citation statements)

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“…To achieve such embedding one has to replace the vertex and edge group with their images in Π 1 pG, Γq (see [15] for details). Since we consider here splittings of pro-p groups as a graph of pro-p groups, we take a different approach developed in [1] to define Π 1 pG, Γ, vq with respect to a base point that gives the embedding above automatically.…”

Section: Fundamental Pro-p Group Of a Profinite Graph Of Pro-p Groupsmentioning

confidence: 99%

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

Mattheus¹,

Zalesski²

2021

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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 in [25] 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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Section: Fundamental Pro-p Group Of a Profinite Graph Of Pro-p Groupsmentioning

confidence: 99%

“…There is a natural continuous action of G on S given by gpg 1 Πpmqq " gg 1 Πpmq, where g, g 1 P G, m P Γ. Clearly GzS " Γ.…”

Section: Standard Pro-p Treementioning

confidence: 99%