Vol. 28, No. 3, 1969

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Automorphisms of groups of similitudes over F3

Jon F. Carlson

Vol. 28 (1969), No. 3, 485–488

Let Q(x) be a quadratic form defined on a vector space M of dimension n = 2m > 4(n8) 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 = ρL (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
Received: 5 March 1968
Published: 1 March 1969
Jon F. Carlson
Department of Mathematics
University of Georgia
Athens GA 30602
United States