University of IsfahanInternational Journal of Group Theory2251-765013220240601Gow-Tamburini type generation of the special linear group for some special rings.1231322760410.22108/ijgt.2023.134366.1800ENNaresh VasantAfreDepartment of Mathematics, University of Mumbai, Mumbai, India0000-00030004-3783Anuradha S.GargeDepartment of Mathematics, University Mumbai, Kalina Campus, Mumbai, India0000-0001-9276-3985Journal Article20220802Let $R$ be a commutative ring with unity and let $n\geq 3$ be an integer. Let $SL_n(R)$ and $E_n(R)$ denote respectively the special linear group and elementary subgroup of the general linear group $GL_n(R).$ 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 $E_n(R)$ (and hence $SL_n(R)$) a set of Gow-Tamburini matrix generators, depending on the minimal number of generators of $R$ as a $Z$-module.https://ijgt.ui.ac.ir/article_27604_4f939f1e06e3ae85b351097196d61860.pdf