Bounded Generation for SL_n(Λ)

2025/04/21 by Avni, Nir, Meiri, Chen
#20G30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.15383

Abstract

Let Λ be an order in a division algebra over a number field. We prove, under some conditions, that SL₃(Λ) is boundedly generated by elementary matrices.

Citations

• Conjugacy width in uniform higher rank arithmetic groups of orthogonal type
• Non-virtually abelian anisotropic linear groups are not boundedly generated
• The verbal width of acylindrically hyperbolic groups is infinite
• Word maps and Waring type problems
• On finitely generated profinite groups II, products in quasisimple groups
• On finitely generated profinite groups I: strong completeness and uniform bounds
• Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields
• Bounded generation of SL(n,A) (after D. Carter, G. Keller and E. Paige)
• On the Commutator Group of a Simple Algebra

Related

• On Multipliers and completely bounded Multipliers -- the case SL(2,R)
• Bounded Generation by semi-simple elements: quantitative results
• On some finite generation properties
• Two-generation of traceless matrices over finite fields
• Growth Rates of Algebras, III: Growth Rates of Solvable Algebras