Direct factors of profinite completions and decidability

Simple item page
dc.creatorBridson, Martin R.
dc.date2008-10-02
dc.date.accessioned2026-07-07T10:07:05Z
dc.date.available2026-07-07T10:07:05Z
dc.descriptionWe consider finitely presented,residually finite groups $G$ and finitely generated normal subgroups $A$ such that the inclusion $A\hookrightarrow G$ induces an isomorphism from the profinite completion of $A$ to a direct factor of the profinite completion of $G$. We explain why $A$ need not be a direct factor of a subgroup of finite index in $G$; indeed $G$ need not have a subgroup of finite index that splits as a non-trivial direct product. We prove that there is no algorithm that can determine whether $A$ is a direct factor of a subgroup of finite index in $G$.
dc.descriptionTo appear in the Journal of Group Theory
dc.identifierhttps://arxiv.org/abs/0810.0399
dc.identifierhttp://arxiv.org/abs/0810.0399
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170510
dc.subjectGroup Theory
dc.subject20E18, 20F10
dc.titleDirect factors of profinite completions and decidability
dc.typetext

Files

Collections

arXiv