Profinite completion and double-dual : isomorphisms and counter-examples

dc.creatorBardavid, Colas
dc.date2008-01-18
dc.date.accessioned2026-07-07T08:55:23Z
dc.date.available2026-07-07T08:55:23Z
dc.descriptionWe define, for any group $G$, finite approximations ; with this tool, we give a new presentation of the profinite completion $\hatπ : G \to \hat{G}$ of an abtract group $G$. We then prove the following theorem : if $k$ is a finite prime field and if $V$ is a $k$-vector space, then, there is a natural isomorphism between $\hat{V}$ (for the underlying additive group structure) and the additive group of the double-dual $V^{**}$. This theorem gives counter-examples concerning the iterated profinite completions of a group. These phenomena don't occur in the topological case.
dc.identifierhttps://arxiv.org/abs/0801.2955
dc.identifierhttp://arxiv.org/abs/0801.2955
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146255
dc.subjectGroup Theory
dc.subject20B, 20E18
dc.titleProfinite completion and double-dual : isomorphisms and counter-examples
dc.typetext

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