Abstract
Let be the ring of -integers in a number field . We prove that if the group of units is infinite then every matrix in is a product of at most 9 elementary matrices. This essentially completes a long line of research in this direction. As a consequence, we obtain a new proof of the fact that is boundedly generated as an abstract group that uses only standard results from algebraic number theory.
Citation
Aleksander V. Morgan. Andrei S. Rapinchuk. Balasubramanian Sury. "Bounded generation of $\mathrm{SL}_2$ over rings of $S$-integers with infinitely many units." Algebra Number Theory 12 (8) 1949 - 1974, 2018. https://doi.org/10.2140/ant.2018.12.1949
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