Orientably regular maps with given exponent group

We prove that for every integer d ≥ 3 and every group U of units mod d, there exists an orientably-regular map of valency d with exponent group U

Chiral maps of given hyperbolic type on AkA_k

This paper proves the existence of a chiral map with alternating automorphism group for every hyperbolic type. We present a set of constructions using permutations for when at least one parameter is even, and call on previously known results for when both the valency and the face-length are odd.Comment: 19 pages, 10 figures, 1 tabl