Groups with essential dimension one

摘要

Denote by ed(K)(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 ed(K)(G) = 1 [Compositio Math. 106 (1997), Theorem 6.2]. We will prove a generalization of this theorem when K is an arbitrary field.