Telescopic groups and symmetries of combinatorial maps
In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given automorphism group. This enhances the already known results by Cori -- Machi, Siran -- Skoviera, and other authors. We also provide a more universal technique for showing that `any automorphism group is possible', that is applicable to a wider classes or, in contrast, to more particular sub-classes of said combinatorial and geometric objects. Finally, we show that any given automorphism group can be realised by sufficiently many such non-isomorphic entities (super-exponentially many with respect to a certain combinatorial complexity measure).