TY - JOUR
ID - 27604
TI - Gow-Tamburini type generation of the special linear group for some special rings.
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Afre, Naresh Vasant
AU - Garge, Anuradha S.
AD - Department of Mathematics, University of Mumbai, Mumbai, India
AD - Department of Mathematics, University Mumbai, Kalina Campus, Mumbai, India
Y1 - 2024
PY - 2024
VL - 13
IS - 2
SP - 123
EP - 132
KW - Quadratic extensions
KW - ring of integers of number fields
KW - special linear group
KW - Elementary subgroup
DO - 10.22108/ijgt.2023.134366.1800
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_27604.html
L1 - https://ijgt.ui.ac.ir/article_27604_4f939f1e06e3ae85b351097196d61860.pdf
ER -