Geodesic
Each finite group is a symmetry group of some map (an “Atom”-bifurcation)
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 21-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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Maps are studied, i.e. cell decompositions of closed two-dimensional surfaces, or two-dimensional atoms, which encode bifurcations of Liouville fibrations of nondegenerate integrable Hamiltonian systems. Any finite group $G$ is proved to be the symmetry group of an orientable map (of an atom). Moreover one such a map $X(G)$ is constructed algorithmically. Upper bounds are obtained for the minimal genus M$g(G)$ of an orientable map with the given symmetry group $G,$ and for the minimal number of vertices, edges and sides of such maps. 
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E. A. Kudryavtseva; A. T. Fomenko. Each finite group is a symmetry group of some map (an “Atom”-bifurcation). Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 21-29. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a2/

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