论文标题
每个有限的阿贝尔组都是有限简单左支架添加剂组的子组
Every finite abelian group is a subgroup of the additive group of a finite simple left brace
论文作者
论文摘要
Rump引入的左括号已在研究量子Yang-Baxter方程的设定理论解决方案的研究中提供了重要的工具。特别是，他们允许建造几个新的解决方案家庭。左撑杆$（b，+，\ cdot）$是由$ b $的两个组结构确定的结构：一个Abelian Group $（b，+）$和一个组$（B，\ CDOT）$，满足某些兼容性条件。本文的主要结果表明，每个有限的Abelian Group $ a $都是带有Abelian Sylow子组的Metabelian乘法组的有限简单的左支架$ B $的亚组的子组。该结果补充了作者在大量有限的简单左括号中的意外结果。
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.
