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Structure of Chevalley groups over rings via universal localization.
- Source :
-
Journal of Algebra . Mar2016, Vol. 450, p522-548. 27p. - Publication Year :
- 2016
-
Abstract
- In the current article we study the structure of a Chevalley group G ( R ) over a commutative ring R . We generalize and improve the following results on: • the standard, relative, and multi-relative commutator formulas; • the nilpotent structure of [relative] K 1 ; • the bounded word length of commutators. To this end we enlarge the elementary group, construct a generic element for the extended elementary group, and use localization in the universal ring. The key step is a construction of a generic element for the principal congruence subgroup, corresponding to a principal ideal. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 450
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 112630454
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2015.11.031