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- Title
GOW-TAMBURINI TYPE GENERATION OF THE SPECIAL LINEAR GROUP FOR SOME SPECIAL RINGS.
- Authors
AFRE, NARESH VASANT; GARGE, ANURADHA S.
- Abstract
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.
- Subjects
FINITE simple groups; ALGEBRAIC numbers; RINGS of integers; ALGEBRAIC fields; GROUP theory; COMMUTATIVE rings
- Publication
International Journal of Group Theory, 2024, Vol 13, Issue 2, p123
- ISSN
2251-7650
- Publication type
Article
- DOI
10.22108/ijgt.2023.134366.1800