Units of commutative modular group algebras
نویسندگان
چکیده
منابع مشابه
Symmetric 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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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...
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Let S(RG) be a normed Sylow p-subgroup in a group ring RG of an abelian group G with p-component Gp and a p-basic subgroup B over a commutative unitary ring R with prime characteristic p. The first central result is that 1 + I(RG;Bp) + I(R(p)G;G) is basic in S(RG) and B[1 + I(RG;Bp) + I(R(p )G;G)] is p-basic in V (RG), and [1 + I(RG;Bp) + I(R(p )G;G)]Gp/Gp is basic in S(RG)/Gp and [1 + I(RG;Bp)...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1994
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)90031-0