单位群是幂的群代数
Group algebras whose group of units is powerful
摘要：
一个p-群称为幂群，如果当p为奇数时，每个交换子都是p次幂的乘积，当p=2时，每个交换子都是4次幂的乘积。在特征为p的有限域上p次幂阶群G的群代数中，正规化单位群总是p群.我们证明，它从来没有强大的，当然，除了当G是阿贝尔。
英文摘要：
A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
