A stabilizer Lemma for translation generalized quadrangles
Let \(F\) be a semifield flock of the finite projective space \(\text{PG}(3,q^n)\), where \(q\) is odd. The author proves that \(F\) is linear if the order of the automorphism group of \(F\) is divisible by \(q^n (q^n +1)\). As a consequence, he obtains the following result for a certain class of translation generalized quadrangles \(S\) of order \((s, s^2)\) where \(s\) is odd: if the collineation group of \(S\) acts transitively on the subquadrangles of \(S\) of order \(s\), then \(S\) is isomorphic to the classical generalized quadrangle \(Q(5,s)\).
scientific article; zbMATH DE number 5077681