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 language | English |
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Journal | Canadian Journal of Mathematics |
DOIs | |
State | Accepted/In press - 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), 2024.
Keywords
- Chevalley groups
- Dedekind rings
- bounded generation