On properties of n-totally projective abelian p -groups - Danchev, P. V.; Keef, P. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We prove some properties of $n$-totally projective abelian $p$-groups. Under some additional conditions for the group structure, we obtain an equivalence between the notions of $n$-total projectivity and strong $n$-total projectivity. We also show that $n$-totally projective $A$-groups are isomorphic if they have isometric $p^n$-socles.