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(\sqrt{q}-1), then U is an ovoidal Buekenhout-Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout-Metz unitals are given.
Group theoretic characterizations of Buekenhout–Metz unitals in PG(2,q^2) / Donati, Giorgio; Durante, Nicola. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - 33:3(2011), pp. 401-407. [10.1007/s10801-010-0250-8]
Group theoretic characterizations of Buekenhout–Metz unitals in PG(2,q^2)
DONATI, GIORGIO;DURANTE, NICOLA
2011
Abstract
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(\sqrt{q}-1), then U is an ovoidal Buekenhout-Metz unital. From this result two group theoretic characterizations of orthogonal Buekenhout-Metz unitals are given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
