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 ¯ , r ¯ , ℓ ¯ ) of PSL ( 3 , p ) such that t ¯ ℓ ¯ = ℓ ¯ t ¯ .
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