On finite approximations of groups and algebras
type: Item
instance of: scholarly article
title: On finite approximations of groups and algebras
zbMATH Open document ID: 1025.20001
author: Miloš Ziman
published in: Illinois Journal of Mathematics
publication date: 2003-11-19T00:00:00Z
review text: A group \(G\) is said to be an LEF group, i.e. \(G\) is locally embeddable into the class of finite groups, if for every finite subset \(M\subseteq G\) there exists a finite group \(H\) and an injective map \(\psi\colon M\cup M^2\to H\) such that \(\psi(x)\psi(y)=\psi(xy)\) for all \(x,y\in M\). In a similar way is defined the class of LEF algebras. Let \(\mathbb{C} G\) be the group algebra of a group \(G\) over the field \(\mathbb{C}\) of the complex numbers. The main result of this paper asserts that \(\mathbb{C} G\) is an LEF algebra if and only if \(G\) is an LEF group.
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20E25
zbMATH DE Number: 1865535
zbMATH Keywords: LEF groups
zbMATH Keywords: locally embeddable into finite groups
zbMATH Keywords: LEF algebras
zbMATH Keywords: group algebras
reviewed by: S. V. Mihovski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1865535