ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS

- Journal title : Journal of the Korean Mathematical Society
- Volume 50, Issue 2, 2013, pp.307-330
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2013.50.2.307

Title & Authors

ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS

Keef, Patrick W.; Danchev, Peter V.;

Keef, Patrick W.; Danchev, Peter V.;

Abstract

If and are non-negative integers, then three new classes of abelian -groups are defined and studied: the , -simply presented groups, the , -balanced projective groups and the , -totally projective groups. These notions combine and generalize both the theories of simply presented groups and -projective groups. If , , these all agree with the class of totally projective groups, but when , they also include the -projective groups. These classes are related to the (strongly) n-simply presented and (strongly) -balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than are characterized, and if in addition we have , they are determined by isometries of their -socles.

Keywords

abelian p-groups;m, n-simply presented groups;m, n-balanced projective groups;m, n-totally projective groups;summable groups;

Language

English

Cited by

2.

3.

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