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arXiv · 2001.08905

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

F. Cedo·E. Jespers·J. Okninski
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Abstract

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 $(B,+,\cdot )$ is a structure determined by two group structures on a set $B$: an abelian group $(B,+)$ and a group $(B,\cdot)$, 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.

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F. Cedo, E. Jespers, J. Okninski. 2020-01-24. Every finite abelian group is a subgroup of the additive group of a finite simple left brace. https://arxiv.org/abs/2001.08905

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