Generating adjoint groups

2018/05/19 by Greenfeld, Be'eri
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1805.07664

Abstract

We prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated, and on the other hand construct a finitely generated, infinite dimensional nil algebra whose adjoint group is generated by elements of bounded torsion.

Related

• Lie algebras and torsion groups with identity
• Adjoint rings are finitely generated
• Finite generation of adjoint rings after Lazic: an introduction
• Adjoint groups of p-nil rings and p-group automorphisms
• Decomposability of Finitely Generated Torsion-free Nilpotent Groups