Orientably-regular p-maps and regular p-maps

Abstract

A map is called a p-map if it has a prime p-power vertices. An orientably-regular (resp. A regular) p-map is called solvable if the group G+ of all orientation-preserving automorphisms (resp. the group G of automorphisms) is solvable; and called normal if G+ (resp. G) contains the normal Sylow p-subgroup.In this paper, it will be proved that both orientably-regular p-maps and regular p-maps are solvable and except for few cases that p∈{2,3}, they are normal. Moreover, nonnormal p-maps will be characterized and some properties and constructions of normal p-maps will be given.