منابع مشابه
Identifications in Modular Group Algebras
Let G be a group, S a subgroup of G, and F a field of characteristic p. We denote the augmentation ideal of the group algebra FG by ω(G). The Zassenhaus-Jennings-Lazard series of G is defined by Dn(G) = G ∩ (1 + ω(G)). We give a constructive proof of a Theorem of Quillen stating that the graded algebra associated to FG is isomorphic as an algebra to the enveloping algebra of the restricted Lie ...
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...
متن کاملUnitary units in modular group algebras
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 کاملLie Nilpotency Indices of Modular Group Algebras
Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent then its upper (or lower) Lie nilpotency index is at most |G| + 1, where |G| is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal have already been determined. Here we determine G for which upper (or lower) L...
متن کاملModular Group Algebras with Maximal Lie Nilpotency Indices
In the present paper we give the full description of the Lie nilpo-tent group algebras which have maximal Lie nilpotency indices.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2008
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2008.01.006