On (2,3,7)-generation of maximal parabolic subgroups

Citation
L. Di Martino et Mc. Tamburini, On (2,3,7)-generation of maximal parabolic subgroups, J AUS MAT A, 71, 2001, pp. 187-199
Citations number
5
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
71
Year of publication
2001
Part
2
Pages
187 - 199
Database
ISI
SICI code
0263-6115(200110)71:<187:O(OMPS>2.0.ZU;2-4
Abstract
Let R be a ring with 1 and E-n(R) be the subgroup of GL(n)(R) generated by the matrices I + re(ij), r is an element of R, i not equal j. We prove that the subgroup Pn,((n) over bar) of En+(n) over bar(R) consisting of the mat rices of shape ((A)(B)(O)((A) over bar)), where A is an element of E-n(R), (A) over bar is an element of E-(n) over bar(R) and B is an element of Mat( n,(n) over bar)(R), is (2, 3, 7)-generated whenever R is finitely generated and n,(n) over bar are large enough.