标题： 新的IYB群类 显示英文标题

标题： New classes of IYB groups

摘要： 证明了所有Sylow子群的幂零类至多为二的奇数阶有限群都是内合Yang-Baxter群（简称IYB群），即它具有一个左brace结构。还证明了所有偶数阶有限可解群，若其所有Sylow子群的幂零类至多为二且Sylow 2-子群为交换群，则也是IYB群。这些结果有助于解决关于哪些有限可解群是IYB群的开放问题，特别是推广了Ben David和Ginosar关于具有交换Sylow子群的有限可解群的结果。 使用相同的技术还证明了所有Sylow子群幂零类至多为二的有限可解群都同构于一类幂零型斜左brace的乘法群。此外，还证明了每个具有Sylow塔性质的有限群都同构于一类幂零型斜左brace的乘法群。 显示英文摘要

摘要： It is proven that every finite group of odd order with all Sylow subgroups of nilpotency class at most two is an involutive Yang-Baxter group (IYB group for short), i.e. it admits a structure of left brace. It is also proven that every finite solvable group of even order with all Sylow subgroups of nilpotency class at most two and abelian Sylow 2-subgroups is an IYB group. These results contribute to the open problem asking which finite solvable groups are IYB, in particular they generalize a result of Ben David and Ginosar concerned with finite solvable groups with abelian Sylow subgroups. With the same techniques it is proven that every finite solvable group with all Sylow subgroups nilpotent of class at most two is isomorphic to the multiplicative group of a skew left brace of nilpotent type. It is also proven that every finite group with the Sylow tower property is isomorphic to the multiplicative group of a skew left brace of nilpotent type.