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arXiv · 1511.02906

Decompositions of congruence subgroups of Chevalley groups

Sergey Sinchuk·Andrei Smolensky
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Abstract

We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in terms of several families of generators. Some of our results are new even in the absolute case and were previously studied only for groups over finite fields.

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Sergey Sinchuk, Andrei Smolensky. 2018-09-29. Decompositions of congruence subgroups of Chevalley groups. https://doi.org/10.1142/s0218196718500418

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