On unitals in $$PG(2,q^2)$$ P G ( 2 , q 2 ) stabilized by a homology group

Abstract

The linear collineation group of a classical unital of $$\mathrm{PG}(2,q^2)$$ PG ( 2 , q 2 ) contains a group of homologies of order $$q+1$$ q + 1 . In this paper we prove that if $$\mathcal{U }$$ U is a unital of PG $$(2,q^2)$$ ( 2 , q 2 ) stabilized by a homology group of order $$q+1$$ q + 1 and $$q$$ q is a prime number, then $$\mathcal{U }$$ U is classical.