Group algebras whose group of units is powerful
Rings and Algebras
2009-06-05 v1 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0906.0870,
title = {Group algebras whose group of units is powerful},
author = {V. A. Bovdi},
journal= {arXiv preprint arXiv:0906.0870},
year = {2009}
}
Comments
4 pages