Braces whose additive group has a cyclic maximal subgroup  

作　　者：Pujin LI Lijuan HE Xinyuan ZHANG 

机构地区：[1]School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan,030031,China

出　　处：《Frontiers of Mathematics in China》2022年第6期1051-1061,共11页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11771258,11801341);the Science Foundation of Shanxi Normal University(Grant No.2019XSY019).

摘　　要：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 odd prime.In this paper we prove Soc(H)≠1 and classify all right braces H such that│Soc(H)│=p^(n-1).

关 键 词：BRACE finite p-groupe Yang-Baxter equation 

分 类 号：O152.1[理学—数学]