منابع مشابه
Group Actions and Group Extensions
In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p)r acts freely on (S1)k , then r ≤ k.
متن کاملCohomology 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...
متن کاملGroup Extensions and Automorphism Group Rings
We use extensions to study the semi-simple quotient of the group ring FpAut(P ) of a finite p-group P . For an extension E : N → P → Q, our results involve relations between Aut(N), Aut(P ), Aut(Q) and the extension class [E] ∈ H(Q,ZN). One novel feature is the use of the intersection orbit group Ω([E]), defined as the intersection of the orbits Aut(N) · [E] and Aut(Q) · [E] in H(Q,ZN). This gr...
متن کاملMagnetic translation group as group extensions
The idea of magnetic translation groups, appearing in considerations of movement of electron in an external magnetic field, was proposed independently by Brown [1] and Zak [2]. From those works follows that the magnetic translation group is an image of Weyl–Heisenberg group [3] obtained by imposing the Born–von Kármán periodic boundary conditions. The general description of similar problems has...
متن کاملGroup Extensions over Infinite Words
We construct an extension E(A,G) of a given group G by infinite nonArchimedean words over an discretely ordered abelian group like Z. This yields an effective and uniform method to study various groups that ”behave like G”. We show that the Word Problem for f.g. subgroups in the extension is decidable if and only if and only if the Cyclic Membership Problem in G is decidable. The present paper ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1963
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1963.13.73