On the cohomology of central Frattini extensions
نویسندگان
چکیده
منابع مشابه
On central Frattini extensions of finite groups
An extension of a group A by a group G is thought of here simply as a group H containing A as a normal subgroup with quotient H/A isomorphic to G. It is called a central Frattini extension if A is contained in the intersection of the centre and the Frattini subgroup of H . The result of the paper is that, given a finite abelian A and finite G, there exists a central Frattini extension of A by G...
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Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...
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A. Brumer has shown that every profinite group of strict cohomological p-dimension 2 possesses a class field theory the tautological class field theory. In particular, this result also applies to the universal p-Frattini extension G̃p of a finite group G. We use this fact in order to establish a class field theory for every p-Frattini extension π : G̃ → G (Thm.A). The role of the class field modu...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولCohomology of Group Extensions
Introduction. Let G be a group, K an invariant subgroup of G. The purpose of this paper is to investigate the relations between the cohomology groups of G, K, and G/K. As in the case of fibre spaces, it turns out that such relations can be expressed by a spectral sequence whose term E2 is HiG/K, HiK)) and whose term Em is the graduated group associated with i7(G). This problem was first studied...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2001
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00117-1