PRIMITIVE ARCS IN PG(2,Q)

We show that a complete are K in the projective plane PG(2, q) admitti ng a transitive primitive group of projective transformations is eithe r a cyclic are of prime order or a known are. If the completeness assu mption is dropped, then K has either an affine primitive group, or K i s contained in an explicit list. In order to find these primitive arcs , it is necessary to determine all complete k-arcs fixed by a projecti ve elementary abelian group of order k. As a corollary to our result, we list all complete arcs fixed by a 2-transitive projective group. (C ) 1995 Academic Press, Inc.