Witt#1: The Burnside Theorem [completed, not proofread] Theorem 1, the Burnside theorem ([1], 19.10). Let G be a finite group, and let X and Y be finite G-sets. Then, the following two assertions A and B are equivalent: Assertion A: We have X ∼ = Y , where ∼ = means isomorphism of G-sets.

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a non-commutative C-algebra associated to a bundle E → M , equipped with a compatible connection ∇, which plays the role of the algebra of functions on the infinit...

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. For a recent survey, see Mühlherr [10...

On the Isomorphism Problem of p-Endomorphisms Peter Jong, Ph.D. Department of Mathematics, University of Toronto, 2003 Let X = (X,B, μ, T ) be a measure-preserving system on a Lebesgue probability space. Given a fixed probability vector p = (p1, . . . , ps), we say that X = (X,B, μ, T ) is a pendomorphism if T is s-to-1 a.e. and the conditional probabilities of the preimages are precisely the c...

In this paper, some properties of the dual B-homomorphism are provided, along with natural and fundamental theorem B-homomorphisms for B-algebras. The first third isomorphism theorems B algebra also presented in paper.

In this paper, we study the twisted basic Dolbeault cohomology and transverse hard Lefschetz theorem on a Kähler foliation. And give some properties for $$\Delta _\kappa $$ -harmonic forms prove Kodaira–Serre-type duality isomorphism cohomology.

The main idea of the proof of this Theorem is to study the geometry (and arithmetic) of the modular diagonal quotient surfaces ZN,1 (as introduced in [9]) in the special case N = 11. Now the algebraic surface Z = ZN,1 has a natural model as a variety over Q (cf. §3), and an open subvariety of this turns out to be the coarse moduli space of the moduli functor ZN,1 which classifies isomorphism cl...

We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on a symplectic manifold M and the ring H(M,C((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket ...

A brief comment about items (3) and (4). If H is a subgroup of G the inclusion map is an injective homomorphism from H to G . On the other hand, the image of an injective homomorphism α : H −→ G is a subgroup that is isomorphic to H . So the study of injective homomorphisms is (up to isomorphism) the study of subgroups. After studying subgroups, we defined normal subgroup and showed several equ...