gow-tamburini type generation of the special linear group for some special rings.

Let r be a commutative ring with unity and let n ≥ 3 be an integer. let sln(r) and en(r) denote respectively the special linear group and elementary subgroup of the general linear group gln(r). a result of hurwitz says that the special linear group of size atleast three over the ring of integers of an algebraic number field is finitely generated. a celebrated theorem in group theory states that finite simple groups are two-generated. since the special linear group of size atleast three over the ring of integers is not a finite simple group, we expect that it has more than two generators. in the special case, where r is the ring of integers of an algebraic number field which is not totally imaginary, we provide for en(r) (and hence sln(r)) a set of gow-tamburini matrix generators, depending on the minimal number of generators of r as a z-module.