论文标题
循环中的三个敏捷概念
Three concepts of nilpotence in loops
论文作者
论文摘要
我们介绍了循环理论中超努力的抽象概念，并将其与现有概念相关，即乘法组的核心nillpotence和niltlitence。我们证明，超努力的类别比乘法组的nilpotence类别更大或相等，并结合了现有结果，我们表明，当且仅当其乘法组具有nilpotent时，有限循环是超元素的。我们还提供了一个经典结果和关键成分的新阐述，该回路具有nilpotent乘法组的循环是中心的，并接受了主要的分解。
We introduce the abstract concept of supernilpotence in loop theory, and relate it to existing concepts, namely, central nilpotence and nilpotence of the multiplication group. We prove that the class of supernilpotence is greater or equal than the class of nilpotence of the multiplication group, and combining existing results, we show that a finite loop is supernilpotent if and only if its multiplication group is nilpotent. We also provide a new exposition of a classical result and crucial ingredient, that loops with a nilpotent multiplication group are centrally nilpotent and admit a prime decomposition.
