加群有循环极大子群的柱

Braces Whose Additive Group Has a Cyclic Maximal Subgroup

构造Yang-Baxter方程的非退化对合集论解的问题可归结为构造所有右柱的问题.特别地,所有有限右柱的分类是描述Yang-Baxter方程所有这类解的基础.设H是p_(n)阶右柱,(H,+)≌Z_(p)×Z_(p^(n-1)),其中n≥4,p是奇素数.本文证明了|Soc(H)|≠1,并且给出了|Soc(H)|=p^(n-1)的H的分类.

The problem of constructing all the non-degenerate involutive set theoretic solutions of the Yang-Baxter equation recently has been reduced to the problem of describing all the right braces.In particular,the classification of all finite right braces is fundamental in describing all such solutions of the Yang-Baxter equation.Let H be a right brace of order p_(n),(H,+)≌Z_(p)×Z_(p^(n-1)),where n≥4 and p is an odd prime.In this paper we prove Soc(H)≠1 and classify all right braces H such that|Soc(H)|=p^(n-1).