Regular Maps from Voltage Assignments and Exponent Groups

In the paper is developed a common generalization of two methods of construction of regular maps on surfaces. The first one produces graph covering projections that extend to coverings of regular embeddings of the graphs involved. The second method employs a double covering projection of graphs which, in general, need not be extendable to a covering of regular maps. In a more general approach, the latter property remains preserved but the multiplicity of the graph covering may be arbitrary. As an application, some new regular embeddings ofn-cubes and complete bipartite graphs will be constructed. Several open problems are included.