JOURNAL OF ALGEBRA 122, 13&149 (1989) Collineation Groups Preserving a Unital of a Projective Plane of Odd Order* MAURO BILIOTTI Dipartimento di Matematica, Uniuersitir di Lecce, Via Arnesano, 73100 Lecce, Italia AND GABOR KORCHMAROS lstituto di Matematica, Universitci della Basilicata, Via N. Sauro 34, 85100 Potenza, Italia Communicated by Marshall Hall, Jr. Received October 15, 1986 DEDICATED TO PROFESSOR GUIDO ZAPPA ON THE OCCASION OF HIS SEVENTIETH BIRTHDAY INTRODUCTION A unital embedded in a finite projective plane L7 of order m2 is a sub- structure of I7 which forms a 2 - (m3 + 1, m + 1, 1) design. Unitals first originate in a finite projective plane l7, endowed with a unitary polarity 9. In such a situation the substructure of I7 consisting of absolute points and non-absolute lines of 9 is just a unital embedded in ZZ, as shown by Seib in [20]. Nevertheless there are examples of unitals which are not related to any polarity in the plane [4]. The “classical” unital consists of absolute points and non-absolute lines of a hermitian polarity of a desarguesian plane of order m2. It is left invariant by a collineation group isomorphic to PlYJ(3, m*), which acts 2-transitively on its points. Conversely, Hoffer [ 131 showed that a unital of a projective plane of order m2, which is invariant under a collineation group isomorphic to PSU(3, m2), is classical. Subsequently, Kantor [ 161 proved that if a unital % is invariant under a collineation group G acting transitively on the flags consisting of a point * This research was supported in part by a grant from the M.P.I. 130 0021-8693/89 $3.00 Copyright 0 1989 by Academic Press, Inc All rights of reproduction in any ioorm reserved.