Bounded generation of SL 2 over rings of S-integers with infinitely many units

Authors

Aleksander V. Morgan, University of Virginia
Andrei S. Rapinchuk, University of Virginia
Balasubramanian Sury, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Algebra and Number Theory

Abstract

Let be the ring of S-integers in a number field k. We prove that if the group of units × is infinite then every matrix in Γ = SL 2 (O) 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 Γ is boundedly generated as an abstract group that uses only standard results from algebraic number theory.

First Page

1949

Last Page

1974

DOI

10.2140/ant.2018.12.1949

Publication Date

1-1-2018

Comments

All Open Access, Green

Recommended Citation

Morgan, Aleksander V.; Rapinchuk, Andrei S.; and Sury, Balasubramanian, "Bounded generation of SL 2 over rings of S-integers with infinitely many units" (2018). Journal Articles. 1532.
https://digitalcommons.isical.ac.in/journal-articles/1532