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On the ideal triangulation graph of a punctured surface

Mustafa Korkmaz, Athanase Papadopoulos (2012)

Annales de l’institut Fourier

We study the ideal triangulation graph T ( S ) of an oriented punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T ( S ) is an isomorphism. We also show that the graph T ( S ) of such a surface S , equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured...

On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups

Shrawani Mitkari, Vilas Kharat (2024)

Mathematica Bohemica

In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups G are studied in respect of formation of lattices L ( G ) and sublattices of L ( G ) . It is proved that the collections of all pronormal subgroups of A n and S n do not form sublattices of respective L ( A n ) and L ( S n ) , whereas the collection of all pronormal subgroups LPrN ( Dic n ) of a dicyclic group is a sublattice of L ( Dic n ) . Furthermore, it is shown that L ( Dic n ) and LPrN ( Dic n ) are lower semimodular lattices.

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