Second cohomology groups and finite covers
نویسندگان
چکیده
For Ω an infinite set, k ≥ 2 and W the set of k-sets from Ω, there is a natural closed permutation group Γk which is a non-split extension 0 → Z 2 → Γk → Sym(Ω) → 1. We classify the closed subgroups of Γk which project onto Sym(Ω). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms.
منابع مشابه
On continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
متن کاملOn the Cohomology of Highly Connected Covers of Finite Complexes
Relying on the computation of the André-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra.
متن کاملAnnihilating the Cohomology of Group Schemes
Our goal in this note is to show that cohomology classes with coefficients in finite flat group schemes can be killed by finite covers of the base scheme, and similarly for abelian schemes with “finite covers” replaced by “proper covers.” We apply this result to commutative algebra by giving a new and more conceptual proof of Hochster-Huneke’s theorem on the existence of big Cohen-Macaulay alge...
متن کاملOn the cohomology of highly connected covers of finite Hopf spaces
Relying on the computation of the André–Quillen homology groups for unstable Hopf algebras, we prove that if the mod p cohomology of both the fiber and the base in an H -fibration is finitely generated as algebra over the Steenrod algebra, then so is the mod p cohomology of the total space. In particular, the mod p cohomology of the n-connected cover of a finite H -space is always finitely gene...
متن کاملThe Bogomolov Multiplier of Finite Simple Groups
The subgroup of the Schur multiplier of a finite group G consisting of all cohomology classes whose restriction to any abelian subgroup of G is zero is called the Bogomolov multiplier of G. We prove that if G is quasisimple or almost simple, its Bogomolov multiplier is trivial except for the case of certain covers of PSL(3, 4).
متن کامل