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Local-global principle for congruence subgroups of Chevalley groups

Himanee Apte, Alexei Stepanov (2014)

Open Mathematics

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...

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.

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