• Korean Journal of Mathematics
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• v.22 no.3
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• pp.501-516
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• 2014

We define the class of almost ${\omega}_1-p^{\omega+n}$-projective abelian p-primary groups and investigate their basic properties. The established results extend classical achievements due to Hill (Comment. Math. Univ. Carol., 1995), Hill-Ullery (Czech. Math. J., 1996) and Keef (J. Alg. Numb. Th. Acad., 2010).

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.401-419
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• 2013

Let $n{\geq}0$ be an arbitrary integer. We define the class of almost n-simply presented abelian p-groups. It naturally strengthens all the notions of almost simply presented groups introduced by Hill and Ullery in Czechoslovak Math. J. (1996), n-simply presented p-groups defined by the present author and Keef in Houston J. Math. (2012), and almost ${\omega}_1-p^{{\omega}+n}$-projective groups developed by the same author in an upcoming publication [3]. Some comprehensive characterizations of the new concept are established such as Nunke-esque results as well as results on direct summands and ${\omega}_1$-bijections.