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

Title & Authors
ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS
Keef, Patrick W.; Danchev, Peter V.;

Abstract
If $\small{m}$ and $\small{n}$ are non-negative integers, then three new classes of abelian $\small{p}$-groups are defined and studied: the $\small{m}$, $\small{n}$-simply presented groups, the $\small{m}$, $\small{n}$-balanced projective groups and the $\small{m}$, $\small{n}$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $\small{p^{w+n}}$-projective groups. If $\small{m}$, $\small{n=0}$, these all agree with the class of totally projective groups, but when $\small{m+n{\geq}1}$, they also include the $\small{p^{w+m+n}}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $\small{n}$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than $\small{{\omega}^2}$ are characterized, and if in addition we have $\small{n=0}$, they are determined by isometries of their $\small{p^m}$-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
1.
ON ALMOST n-SIMPLY PRESENTED ABELIAN p-GROUPS,;

Korean Journal of Mathematics, 2013. vol.21. 4, pp.401-419
1.
ON ALMOST n-SIMPLY PRESENTED ABELIAN p-GROUPS, Korean Journal of Mathematics, 2013, 21, 4, 401
2.
On ω1-n-simply presented abelian p-groups, Journal of Algebra and Its Applications, 2015, 14, 03, 1550032
3.
On α-simply presented abelian p-groups, Mathematical Proceedings of the Royal Irish Academy, 2014, 114A, 2, 219
4.
On variations of m,n-simply presented abelian p-groups, Science China Mathematics, 2014, 57, 9, 1771
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