具有交换乘法Sylow子群的单左花括号的丰富性
An abundance of simple left braces with abelian multiplicative Sylow subgroups
摘要：
Rump引入大括号研究了杨-巴克斯特方程的对合非退化集合论解.最近发现了一种构造性的方法，可以从所有有限左支撑的描述中产生所有这样的有限解。因此，构造和分类所有简单左括号是一个基本问题，因为它们可以被认为是一般理论的基石。这个项目最近由Bachiller和作者发起。本文研究了单有限左大括号，使得其乘法群的Sylow子群是交换群。我们提供了几个新的家庭这样简单的左括号。特别是，他们导致了主要的，令人惊讶的结果，这表明有大量这样的简单左括号。
英文摘要：
Braces were introduced by Rump to study involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. A constructive method for producing all such finite solutions from a description of all finite left braces has been recently discovered. It is thus a fundamental problem to construct and classify all simple left braces, as they can be considered as building blocks for the general theory. This program recently has been initiated by Bachiller and the authors. In this paper we study the simple finite left braces such that the Sylow subgroups of their multiplicative groups are abelian. We provide several new families of such simple left braces. In particular, they lead to the main, surprising result, that shows that there is an abundance of such simple left braces.
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