Nonorientable regular maps over linear fractional groups - Jones, Gareth A. (Ars mathematica contemporanea, 2013)
It is well known that for any given hyperbolic pair ?$(k, m)$? there exist infinitely many regular maps of valence ?$k$? and face length ?$m$? on an orientable surface, with automorphism group isomorphic to a linear fractional group. A nonorientable analogue of this result was known to be true for all pairs ?$(k, m)$? as above with at least one even entry. In this paper we establish the existence of such regular maps on nonorientable surfaces for all hyperbolic pairs.
Keywords: linear fractional group.; regular map