Automorphisms of groups of similitudes over F₃

Jon F. Carlson

Vol. 28 (1969), No. 3, 485–488

DOI: 10.2140/pjm.1969.28.485

Abstract

Let Q(x) be a quadratic form defined on a vector space M of dimension n = 2m > 4(n≠8) over the field with three elements. The purpose of this paper is to show that any automorphism of the projective group of similitudes or of the projective group of proper similitudes can not take the coset of an (n − 2,2) involution into the coset of an (n − p,p) involution or into the coset of a similitude T of ratio ρ where T² = ρ_L (left multiplication by ρ) and where ρ is not a square in F₃. This result, together with some results of Wonenburger, shows that any such automorphism is induced by an automorphism of the group of similitudes.

Mathematical Subject Classification

Primary: 20.22

Milestones

Received: 5 March 1968

Published: 1 March 1969