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On chirality groups and regular coverings of regular oriented hypermaps

Antonio Breda d'Azevedo, Ilda Inácio Rodrigues, Maria Elisa Fernandes (2011)

Czechoslovak Mathematical Journal

We prove that if the Walsh bipartite map = 𝒲 ( ) of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps ( 3 , 3 , 3 ) b , c = 𝒲 - 1 { 6 , 3 } b , c induced by the family of toroidal bipartite maps...

On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki (1992)

Fundamenta Mathematicae

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

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