Orchestrating a powerful group

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Group Algebras Whose Group of Units Is Powerful

A p-group is called powerful if every commutator is a product of p th 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.

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ژورنال

عنوان ژورنال: Science

سال: 2016

ISSN: 0036-8075,1095-9203

DOI: 10.1126/science.352.6283.378