2022/10/16 by Ilaria Colazzo, Maria Ferrara, Colazzo, Ilaria +3 · 5 citations
Materials Science · Mathematics · #08A05 #16Nxx #16T25 #20F24 #81R50 #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Magnetism in coordination complexes #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.08598
openalex publication_date 2022/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If (X,r) is a finite non-degenerate set-theoretic solution of the Yang--Baxter equation, the additive group of the structure skew brace G(X,r) is an FC-group, i.e. a group whose elements have finitely many conjugates. Moreover, its multiplicative group is virtually abelian, so it is also close to an FC-group itself. If one additionally assumes that the derived solution of (X,r) is indecomposable, then for every element b of G(X,r) there are finitely many elements of the form b*c and c*b, with c∈ G(X,r). This naturally leads to the study of a brace-theoretic analogue of the class of FC-groups. For this class of skew braces, the fundamental results and their connections with the solutions of the YBE are described: we prove that they have good torsion and radical theories and they behave well with respect to certain nilpotency concepts and finite generation.