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Displaying similar documents to “Peripheral separability and cusps of arithmetic hyperbolic orbifolds.”

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

Oliver Baues, Fritz Grunewald (2006)

Publications Mathématiques de l'IHÉS

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We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain...

On volumes of arithmetic quotients of S O ( 1 , n )

Mikhail Belolipetsky (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of S O ( 1 , n ) . As a result we prove that for any even dimension  n there exists a unique compact arithmetic hyperbolic n -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic...