منابع مشابه
On 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...
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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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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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Let p be a prime, K a field of characteristic p , G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g 7→ g of G extends linearly to KG ; this extension leaves V setwise invariant, and its restriction to V followed by v 7→ v gives an automorphism of V . The elements of V fixed by this automorphism are called unitary; t...
متن کاملGroup Algebras Whose Involutory Units Commute
Abstract. Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V (KG)be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V (KG) commute with each other if and only if G is isomorphic to one of the groups on this list. In particular, this property depends only on G and not ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2001
ISSN: 0092-7872,1532-4125
DOI: 10.1081/agb-100107935