Profinite subgroup accessibility and recognition of amalgamated factors
Julian Wykowski
University of Cambridge, Cambridge, UK
Abstract
We investigate accessible subgroups of a profinite group , that is, subgroups appearing as vertex groups in a graph of profinite groups decomposition of with finite edge groups. We prove that any accessible subgroup arises as the kernel of a continuous derivation of in a free module over its completed group algebra. This allows us to deduce splittings of an abstract group from splittings of its profinite completion. We prove that any finitely generated subgroup of a finitely generated virtually free group whose closure is a factor in a profinite amalgamated product along a finite must be a factor in an amalgamated product along some . This extends previous results of Parzanchevski–Puder, Wilton and Garrido–Jaikin-Zapirain on free factors.
Cite this article
Julian Wykowski, Profinite subgroup accessibility and recognition of amalgamated factors. Groups Geom. Dyn. (2025), published online first
DOI 10.4171/GGD/851