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.
"Groups with Essential Dimension One." Asian J. Math. 12 (2) 177 - 192, June 2008.