Group theoretic characterizations of Buekenhout–Metz unitals in $\mathop{\mathrm{PG}}(2,q^{2})$

Giorgio Donati, Nicola Durante
2010 Journal of Algebraic Combinatorics  
Let G be the group of projectivities stabilizing a unital U in PG(2, q 2 ) and let A, B be two distinct points of U. In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q − 1 greater than 2( √ q − 1), then U is an ovoidal Buekenhout-Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout-Metz unitals are given.
doi:10.1007/s10801-010-0250-8 fatcat:ghlhjk4ma5btzeovcsw6zftd7i