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We define the classes of almost weak  p  ω·2+ n  -projective and almost ω 1 -weak  p  ω·2+ n  -projective  p -primary abelian groups and establish some of their crucial properties. Important generalizations and extensions of classical results are also obtained in this new framework.

On almost ω 1 -weak p ω·2+ n -projective abelian p -groups