Abstract
The main result of the present paper is bounded elementary generation of the Steinberg groups St(Φ,R) for simply laced root systems Φ of rank ⩾2 and arbitrary Dedekind rings of arithmetic type. Also, we prove bounded generation of St(Φ,Fq[t,t-1]) for all root systems Φ, and bounded generation of St(Φ,Fq[t]) for all root systems Φ≠A1. The proofs are based on a theorem on bounded elementary generation for the corresponding Chevalley groups, where we provide uniform bounds.
| Original language | English |
|---|---|
| Article number | 23 |
| Journal | European Journal of Mathematics |
| Volume | 11 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2025 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.
Keywords
- Bounded generation
- Chevalley group
- Dedekind ring
- Stability of K
- Steinberg group
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