论文标题
某些代数中的一项元素的产品
Products of Unipotent Elements in Certain Algebras
论文作者
论文摘要
令$ f $为一个至少三个元素和本地有限的$ g $的字段。本文旨在表明，如果$ f $是代数关闭的，或者$ f $的特征是正面的，那么小组代数$ fg $中的元素是一项单位元素的产物，并且只有当时，它才是吗？位于$ fg $的单位组的第一个派生子组。另外，它吗？最多是三个独立元素的产物。 此外，我们探讨了某些代数满足的一些关键特性，例如索引2和换向器的单位元素之间的连接，以及我们通过表明在无限场上的有限群体的组代数来调查组代数的一能激进。特别是，我们将这些结果应用于扭曲的组代数。
Let $F$ be a field with at least three elements and $G$ a locally finite group. This paper aims to show that if either $F$ is algebraically closed or the characteristic of $F$ is positive, then an element in the group algebra $FG$ is a product of unipotent elements if, and only if, it? lies in the first derived subgroup of the unit group of $FG$. In addition, it? is a product of at most three unipotent elements. Moreover, we explore some crucial properties satisfied by certain algebras like the connection between unipotent elements of index 2 and commutators as well as we investigate the unipotent radical of a group algebra by showing that the group algebra of a finite group over an infinite field cannot have a unipotent maximal subgroup. In particular, we apply these results to twisted group algebras.
