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http://dx.doi.org/10.4134/JKMS.2013.50.2.307

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

Keef, Patrick W. (Department of Mathematics Whitman College)
Danchev, Peter V. (Department of Mathematics Plovdiv University "P. Hilendarski")
Publication Information
Journal of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 307-330 More about this Journal
Abstract
If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.
Keywords
abelian p-groups; m, n-simply presented groups; m, n-balanced projective groups; m, n-totally projective groups; summable groups;
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