GROUPS PSL(3, P) AND NONORIENTABLE REGULAR MAPS

Abstract

A 2-cell embedding of a graph on a nonorientable closed surface is called regular if its automorphism group acts regularly on its flags. This paper gives a classification of nonorientable regular maps with the automorphism groups PSL(3, p) for a prime p. Equivalently, we determine the representatives of orbits of Aut(PSL(3, p)) acting on the set of involutory generating triples ((t) over bar, (r) over bar, (l) over bar) of PSL(3, p) such that (t) over bar(l) over bar = (l) over bar(t) over bar. (c) 2008 Elsevier Inc. All rights reserved.