Uniform bounded elementary generation of Chevalley groups

被引：1

作者：

Kunyavskii, Boris ^{[1
]}

Plotkin, Eugene ^{[1
]}

Vavilov, Nikolai ^{[2
]}

机构：

[1] Bar Ilan Univ, Dept of Math, Ramat Gan, Israel

[2] St Petersburg State Univ, Dept Math & Comp Sci, St Petersburg, Russia

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2024年

关键词：

Chevalley groups; Dedekind rings; bounded generation; RINGS;

D O I：

10.4153/S0008414X24000713

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank >= 2 over arbitrary Dedekind rings R of arithmetic type, with uniform bounds. Namely, we show that for every reduced irreducible root system Phi of rank >= 2, there exists a universal bound L = L (Phi) such that the simply connected Chevalley groups G (Phi, R) have elementary width <= L for all Dedekind rings of arithmetic type R .

引用

页数：28

共 44 条

[21] Bounded generation of SL2 over rings of S-integers with infinitely many units [J].