Structure of Chevalley groups over rings via universal localization

JOURNAL OF ALGEBRA

卷:450

Article

Stepanov, Alexei^1,2 

[1] St Petersburg State Univ, Dept Math & Mech, Univ Sky 28, St Petersburg 198504, Russia

[2] St Petersburg State Electrotech Univ, Prof Popova 5, St Petersburg 197376, Russia

关键词: Chevalley group;    Commutator formula;    Elementary subgroup;    Nilpotent structure;    Word length;    Principal congruence subgroup;    Localization;   

DOI  :  10.1016/j.jalgebra.2015.11.031

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free