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UDC 512.541.3

# ON SUBGROUPS OF THE DIRECT SUM OF INFINITE CYCLIC ABELIAN GROUPS

Trukhmanov Vyacheslav Borisovich

Arzamas branch of the Lobachevsky State University of Nizhni Novgorod

Candidate of physico-mathematical Sciences, associate Professor

Arzamas branch of the Lobachevsky State University of Nizhni Novgorod

Candidate of physico-mathematical Sciences, associate Professor

**Abstract**

*Article is devoted to one of the subclasses of Abelian torsion-free groups of rank 2, namely, Abelian groups that are subdirect sum of two infinite cyclic groups generated by a finite cyclic group (such groups are called elementary special). The problem of describing Abelian groups of finite rank, than the rank 1 (for groups of rank 1, the problem is solved), is sufficiently important and actively solved in the theory of Abelian groups. Consider some properties of groups of this subclass, as well as the set of all elementary special groups for different groups of generators.*

**Keywords:** Abelian group, Abelian torsion-free, infinite cyclic group, subdirect sum of Abelian groups, the ring of integers, the ring of residues

**Category:** Mathematics

**Article reference:**

Trukhmanov V.B. On subgroups of the direct sum of infinite cyclic Abelian groups // Researches in Science. 2014. № 7 [Electronic journal]. URL: https://science.snauka.ru/en/2014/07/8259

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