On prime order automorphisms of generalized quadrangles

Abstract

In this paper, we study prime order automorphisms of generalized quadrangles. We show that, if Q is a thick generalized quadrangle of order (s, t), where s > t and s + 1 is prime, and Q has an automorphism of order s + 1, then s t

On finite generalized quadrangles with $\mathrm{PSL}(2,q)$ as an automorphism group

“…Lemma 2.3. ( [26, 2.4.1], [1,Lemma 2.5]) Let g be an automorphism of a generalized quadrangle S = (P, B, I) of order (s, t). Let P g and B g be the set of fixed points and fixed lines of g respectively, and set I g := I ∩ P g × B g , S g := (P g , B g , I g ).…”