Year: 2008
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Bardavid, Colas
Institution: Institut de recherche mathématique de Rennes
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1825660452