The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Determination of all regular maps of small genus
Journal of Combinatorial Theory Series B
Families of regular graphs in regular maps
Journal of Combinatorial Theory Series B
Regular homomorphisms and regular maps
European Journal of Combinatorics
Regular maps whose groups do not act faithfully on vertices, edges, or faces
European Journal of Combinatorics - Special issue: Topological graph theory II
Journal of Combinatorial Theory Series B
Realizing finite edge-transitive orientable maps
Journal of Graph Theory
Map operations and k-orbit maps
Journal of Combinatorial Theory Series A
Regular maps with nilpotent automorphism groups
European Journal of Combinatorics
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The parallel product of two rooted maps was introduced by S.E. Wilson in 1994. The main question of this paper is whether for a given reflexible map M one can decompose the map into a parallel product of two reflexible maps. This can be achieved if and only if the monodromy (or the automorphism) group of the map has at least two minimal normal subgroups. All reflexible maps up to 100 edges, which are not parallel-product decomposable, are calculated and presented. For this purpose, all degenerate and slightly-degenerate reflexible maps are classified. In this paper the theory of F-actions is developed including a classification of quotients and parallel-product decomposition. Projections and lifts of automorphisms for quotients and for parallel products are studied. The theory can be immediately applied on rooted maps and rooted hypermaps as they are special cases of F-actions.