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GROUP ALGEBRAS WHOSE GROUP OF UNITS IS POWERFUL
Published online by Cambridge University Press: 15 December 2009
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.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 325 - 328
- Copyright
- Copyright © Australian Mathematical Publishing Association, Inc. 2009