@article {
author = {Afre, Naresh and Garge, Anuradha},
title = {Gow-Tamburini type generation of the special linear group for some special rings.},
journal = {International Journal of Group Theory},
volume = {13},
number = {2},
pages = {123-132},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2023.134366.1800},
abstract = {Let $R$ 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.},
keywords = {Quadratic extensions,ring of integers of number fields,special linear group,Elementary subgroup},
url = {https://ijgt.ui.ac.ir/article_27604.html},
eprint = {https://ijgt.ui.ac.ir/article_27604_4f939f1e06e3ae85b351097196d61860.pdf}
}