Bounded generation of some -arithmetic orthogonal groups

Elementary Subgroups of Relatively Hyperbolic Groups and Bounded Generation

“…Many lattices in semi-simple Lie groups of R-rank at least 2 are known to be boundedly generated. For instance, Carter and Keller [5] established bounded generation for SL n (O), where O is the ring of integers of a number field and n ≥ 3 (see also [1] for an elementary proof in case O = Z and [6,11,21] for other results).…”

On bounded cohomology of amalgamated products of groups

“…(See [3] for a simple proof of triviality of H 2 b,2 for Chevalley groups over rings of S-integers in algebraic number fields using bounded generation.) For example, Grigorchuk [7] (cf.…”

Bounded Generation of Two Families of S-Arithmetic Groups

“…This is the main theorem of [7] Assume K is an algebraic number field and let S be a finite subset of V K containing…”

“…In this section we define properties that are used in [6] to show that some orthogonal groups have bounded generation. In the next section we introduce analogous properties for unitary groups.…”

“…(We refer to Section 0.1 for all unexplained notations.) In this case Rapinchuk and Erovenko showed in [7] that Spin(V ) O S (and thus the corresponding orthogonal group) has bounded generation. In Chapter 3 we extend their method to establish bounded generation for certain unitary groups.…”