منابع مشابه
Twisted automorphisms of group algebras
We continue the study of twisted automorphisms of Hopf algebras started in [4]. In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra of a group of order coprime to 6. The description turns out to be very similar to the one for the universal enveloping algebra given in [4].
متن کاملOn Symmetric Units in Group Algebras
Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K . The anti-automorphism g 7→ g of G can be extended linearly to an anti-automorphism a 7→ a∗ of KG . Let S∗(KG) = {x ∈ U(KG) | x∗ = x} be the set of all symmetric units of U(KG) . We consider the following question: for which groups G and commutative rings K it is true that S∗(KG) is a subgroup in U(KG...
متن کاملTwisted Group Rings Whose Units Form an Fc-group
Let U(KλG) be the group of units of an infinite twisted group algebra KλG over a field K. We describe the maximal FC-subgroup of U(KλG) and give a characterization of U(KλG) with finitely conjugacy classes. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus’ theorem.
متن کاملGroup 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.
متن کاملSymmetric Units in Modular Group Algebras
Let p be a prime, G a locally finite p -group, K a commutative ring of characteristic p . The anti-automorphism g 7→ g of G extends linearly to an anti-automorphism a 7→ a∗ of KG . An element a of KG is called symmetric if a∗ = a . In this paper we answer the question: for which G and K do the symmetric units of KG form a multiplicative group. Let G be a group, K a commutative ring (with 1), an...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9088