Showing papers on "Torsion-free abelian group published in 2016"

A torsion-free abelian group exists whose quotient group modulo the square subgroup is not a \(nil\)-group

Abstract: The first example of a torsion-free abelian group such that the quotient group of modulo the square subgroup is not a nil-group is indicated (for both associative and general rings). In particular, the answer to the question posed by Stratton and Webb [‘Abelian groups, nil modulo a subgroup, need not have nil quotient group’, Publ. Math. Debrecen 27 (1980), 127–130] is given for torsion-free groups. A new method of constructing indecomposable nil-groups of any rank from to is presented. Ring multiplications on -pure subgroups of the additive group of the ring of -adic integers are investigated using only elementary methods.

Canonical and existential groups in universal classes of Abelian groups

Abstract: Universal classes of Abelian groups are classified in terms of sets of finitely generated groups closed with respect to the discrimination operator. The notions of a principal universal class and a canonical group for such a class are introduced. For any universal class K, the class K ec of existentially closed groups generated by the universal theory of K is described. It is proved that K ec is axiomatizable and, therefore, the universal theory of K has a model companion.