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Every finite abelian group is a subgroup of the additive group of a finite simple left brace

Journal Contribution - Journal Article

Left braces, introduced by Rump, have turned out to provide an important tool in the study of set-theoretic solutions of the quantum Yang–Baxter equation. In particular, they have allowed to construct several new families of solutions. A left brace (B,+,⋅) is a structure determined by two group structures on a set B: an abelian group (B,+) and a group (B,⋅), satisfying certain compatibility conditions. The main result of this paper shows that every finite abelian group A is a subgroup of the additive group of a finite simple left brace B with metabelian multiplicative group with abelian Sylow subgroups. This result complements earlier unexpected results of the authors on an abundance of finite simple left braces.

Journal: J. Pure Appl. Algebra
ISSN: 0022-4049
Issue: 1
Volume: 225
Publication year:2021
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
Authors:International
Authors from:Higher Education
Accessibility:Open