On the structure of some nilpotent braces

M.R. Dixon; L.A. Kurdachenko

doi:10.15421/242303

On the structure of some nilpotent braces

M.R. Dixon (University of Alabama)
L.A. Kurdachenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0002-6368-7319

Abstract

We prove a criteria for nilpotency of left braces in terms of the $$$\star$$$-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace $$$A$$$ is Smoktunowicz-nilpotent, then the additive and multiplicative groups of $$$A$$$ are likewise finitely generated.

Keywords

brace; nilpotent brace; soluble brace; Noetherian brace

MSC 2020

16N80; 16T25; 16N40; 20F16

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References

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