On theory of finite subsets monoid for one torsion abelian group

Monoid Kernels and Profinite Topologies on the Free Abelian Group

To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a proonite topology on any nite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can eeectively compute membership in the closure of a subgroup and more generally, in the closure of a rational subset of such a ...

On controllers of prime ideals in group algebras of torsion-free abelian groups of finite rank

Let RA be a group ring of an abelian group A and let I be an ideal of RA . We say that a subgroup B of A controls I if I = (I ∩ RB)RA. The intersection c(I) of all subgroups of A controlling I is said to be the controller of the ideal I ; c(I) is the minimal subgroup of A which controls the ideal I . The ideal I is said to be faithful if I = A ∩ (1 + I) = 1. In theorem 4 we consider some method...

Quasi-half-factorial Subsets of Abelian Torsion Groups

If G is an abelian torsion group with generating subset G0, then by a classical result in the theory of non-unique factorizations, the block monoid B(G0) is a half-factorial monoid if each of its atoms has cross number 1. In this case, G0 is called a half-factorial set. In this note, we introduce the notion of a k-quasihalf-factorial set and show for many abelian torsion groups that G0 k-quasi-...

When Can One Finite Monoid Simulate Another?

On Abelian group representability of finite groups

A set of quasi-uniform random variables X1, . . . , Xn may be generated from a finite group G and n of its subgroups, with the corresponding entropic vector depending on the subgroup structure of G. It is known that the set of entropic vectors obtained by considering arbitrary finite groups is much richer than the one provided just by abelian groups. In this paper, we start to investigate in mo...