Group Algebras Whose Group of Units Is Powerful
نویسنده
چکیده
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.
منابع مشابه
Symmetric Units and Group Identities in Group Algebras. I
We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
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تاریخ انتشار 2009