Profinite completion and double-dual : isomorphisms and counter-examples
| dc.creator | Bardavid, Colas | |
| dc.date | 2008-01-18 | |
| dc.date.accessioned | 2026-07-07T08:55:23Z | |
| dc.date.available | 2026-07-07T08:55:23Z | |
| dc.description | We 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.identifier | https://arxiv.org/abs/0801.2955 | |
| dc.identifier | http://arxiv.org/abs/0801.2955 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146255 | |
| dc.subject | Group Theory | |
| dc.subject | 20B, 20E18 | |
| dc.title | Profinite completion and double-dual : isomorphisms and counter-examples | |
| dc.type | text |