Abelian Rank of Normal Torsion-free Finite Index Subgroups of Polyhedral Groups
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چکیده
Suppose that P is a convex polyhedron in the hyperbolic 3-space with finite volume and P has integer ( > 1) submultiples of it as dihedral angles. We prove that if the rank of the abelianization of a normal torsion-free finite index subgroup of the polyhedral group G associated to P is one, then P has exactly one ideal vertex of type (2,2,2,2) and G has an index two subgroup which does not contain any one of the four standard generators of the stabilizer of the ideal vertex.
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تاریخ انتشار 2010