Theorem 1. Let the countable abelian group G act nonsingularly and aperiodically on Lebesgue space (X, p.). Then for each finite subset A c G and e > 0 3 finite B c G and F tz X with [bF: bEB} disjoint and PKfl meAB a)F] > 1-e. Theorem 2. Every nonsingular action of a countable abelian group on a Lebesgue space is hyperfinite.

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...

In Dhar’s model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges. A local commutativity condition ensures that the final output does not depend on the order in which the automata process their inputs. We consider the halting problem for such networks and the critical group, an invariant that governs the behavior of the network on la...

a group is called morphic if for each normal endomorphism α in end(g),there exists β such that ker(α)= gβ and gα= ker(β). in this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= gβ and gα = ker(γ). we call g quasi-morphic, if this happens for any normal endomorphism α in end(g). we get the following results: g is quasi-morphic if and only if, for any ...

The Kemperman Structure Theorem (KST) yields a recursive description of the structure of a pair of finite subsets A and B of an abelian group satisfying |A + B| ≤ |A| + |B| − 1. In this paper, we introduce a notion of quasi-periodic decompositions and develop their basic properties in relation to KST. This yields a fuller understanding of KST, and gives a way to more effectively use KST in prac...

We present a method for deciding when a regular abelian cover of a finite CWcomplex has finite Betti numbers. To start with, we describe a natural parameter space for all regular covers of a finite CW-complex X, with group of deck transformations a fixed abelian group A, which in the case of free abelian covers of rank r coincides with the Grassmanian of r-planes in H1(X,Q). Inside this paramet...

— In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, the method that we use here enables us to show that, if we ...

— In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, the method that we use here enables us to show that, if we ...

— In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, the method that we use here enables us to show that, if we ...