标题： IYB群的新类 显示英文标题

标题： New classes of IYB groups

摘要： 证明了每个奇数阶的有限群，其所有Sylow子群的幂零类最多为二，则是一个对合Yang-Baxter群（简称为IYB群），即它具有左括号结构。 还证明了每个偶数阶的有限可解群，其所有Sylow子群的幂零类最多为二且Sylow 2子群为交换群，则是一个IYB群。 这些结果有助于解决关于哪些有限可解群是IYB的问题，特别是它们推广了Ben David和Ginosar关于具有交换Sylow子群的有限可解群的结果。 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.