2024/05/07 by A. Ballester‐Bolinches, Ballester-Bolinches, A., R. Esteban‐Romero +5 · 2 citations
Engineering · #16N40 #16T25 #81R50 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2405.04213
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to introduce and study the class of all left braces in which every subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite Dedekind left brace is centrally nilpotent. Structural results about Dedekind left braces and a complete description of those ones whose additive group is elementary abelian are also shown. As a consequence, every hypermultipermutational Dedekind left brace whose additive group is elementary abelian is multipermutational of level 2. A new class of left braces, the extraspecial left braces, is introduced and plays a prominent role in our approach.