Bounded generation of SL_2 over rings of S-integers with infinitely many units

Aleksander V. Morgan, Andrei S. Rapinchuk, Balasubramanian Sury

Let O be the ring of S-integers in a number field k. We prove that if the group of units O^* is infinite then every matrix in $\Gamma$ = SL_2(O) is a product of at most 9 elementary mat…