On ω1-n-simply presented abelian p-groups

Abstract

We define the class of ω1-n-simply presented abelian p-groups which class properly contains the subclasses of n-simply presented groups and ω1-pω+n-projective groups, respectively. Some comprehensive results in this new way are also established. This substantially strengthens achievements due to both Keef–Danchev [On n-simply presented primary abelian groups, Houston J. Math.38(4) (2012) 1027–1050] and Keef [On ω1-pω+n-projective primary abelian groups, J. Algebra Number Theory Acad.1(1) (2010) 41–75].