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Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and...

Maximal Nonparabolic Subgroups of the Modular Group.

J.L. Brenner, R.C. Lyndon (1983)

Mathematische Annalen

Non-minimal modular symbols for GL(n).

Avner Ash (1988)

Inventiones mathematicae

Normal subgroups of classical groups over Banach algebras.

Leonid N. Vaserstein (1988)

Commentarii mathematici Helvetici

Normalizers of Modular Groups.

Morris Newman (1978)

Mathematische Annalen

Normalteiler ganzzahliger Spingruppen.

Martin Kneser (1979)

Journal für die reine und angewandte Mathematik

On a question of M. Conder

M. Chiara Tamburini, Paola Zucca (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that the special linear group $S L (3, Z)$ , over the integers, is not $(2, 3)$ -generated. This gives a negative answer to a question of M. Conder.

On arithmetic Fuchsian groups and their characterizations

Slavyana Geninska (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.

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Free Quotients of Congruence Subgroups of SL2 Over a Coordinate Ring.

Free quotients of finitely presented groups.

Genera of congruence subgroups in Q-quaternion algebras.

Generalization of the symplectic modular group

Homomorphisms of Unitary Groups.

Independent generators for congruence subgroups of Hecke groups.

Kazhdan constants for SL (3, Z).

Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces.

Konstruktionsprinzipien für Untergruppen der Modulgruppen mit einer oder zwei Spitzenklassen.

Local-global principle for congruence subgroups of Chevalley groups