Asian Journal of Mathematics

Volume 12 (2008)

Number 2

Groups with Essential Dimension One

Pages: 177 – 192

DOI: https://dx.doi.org/10.4310/AJM.2008.v12.n2.a2

Authors

Huah Chu

Shou-Jen Hu

Ming-Chang Kang

Jiping Zhang

Abstract

Denote by edK(G) the essential dimension of G over K. If K is an algebraically closed field with char K = 0, Buhler and Reichstein determine explicitly all finite groups G with edK(G) = 1. We will prove a generalization of this theorem when K is an arbitrary field.

Keywords

Essential dimension, compression of finite group actions, Galois theory, finite subgroups of SL_2(K)

2010 Mathematics Subject Classification

12E05, 12F10, 12F20, 13F30

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Published 1 January 2008