Finite groups of essential dimension one
type: Item
instance of: scholarly article
title: Finite groups of essential dimension one
zbMATH Open document ID: 1117.12003
author: Arne Ledet
published in: Journal of Algebra
publication date: 2007-05-03T00:00:00Z
review text: The notion of essential dimension of a finite group \(G\) over a field \(K\) was introduced by \textit{J. Buhler} and \textit{Z. Reichstein} [Compos. Math. 106, 159--179 (1997; Zbl 0905.12003)]. In the paper under review it is shown that a finite group \(G\) has essential dimension 1 over an infinite field \(K\) if and only if there exists an embedding of \(G\) into \(\text{GL}_2(K)\) such that the image of \(G\) contains no scalar matrices other than the identity. The proof goes by reducing the theorem to the case where \(G\) is a \(p\)-group and then distinguishing between the cases where \(p= 2\) and \(p\neq 2\).
Mathematics Subject Classification ID: 12F10
zbMATH DE Number: 5148852
zbMATH Keywords: Galois theory
zbMATH Keywords: essential dimension
zbMATH Keywords: group representations
reviewed by: Christian U. Jensen
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.12.027
OpenAlex ID: W2107726966
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DOI: 10.1016/J.JALGEBRA.2006.12.027
description: scientific article; zbMATH DE number 5148852