Uniform bounded elementary generation of Chevalley groups

Boris Kunyavskiĭ, Eugene Plotkin, Nikolai Vavilov

Research output: Contribution to journalArticlepeer-review

Abstract

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 Φ of rank ≥ 2, there exists a universal bound L = L(Φ) such that the simply connected Chevalley groups G(Φ, R) have elementary width ≤ L for all Dedekind rings of arithmetic type R.

Original languageEnglish
JournalCanadian Journal of Mathematics
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s), 2024.

Keywords

  • Chevalley groups
  • Dedekind rings
  • bounded generation

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