On \(m\)-\(\omega_1\)-\(p^{\omega+n}\)-projective Abelian \(p\)-groups. (Q488819)

This paper is part of a long sequence of the author's in which he generalizes previously studied properties of infinite abelian \(p\)-groups. In this case, his main definition is that \(G\) is \(m\)-\(\omega_1\)-\(p^{\omega+n}\)-projective if \(G\) has a \(p^m\)-bounded subgroup \(A\) such that \(G/A\) is strongly \(\omega_1\)-\(p^{\omega+n}\)-projective, the latter property being one defined in the previous paper in the sequence. He defines a variety of further generalizations by restricting the subgroup \(A\) to lie in various classes of groups. The author then studies the relations among these properties and the inheritance of the properties under the operations \(G\to p^\lambda G\) and \(G\to G/p^\lambda G\) for various ordinals \(\lambda\). The paper concludes with problems suggesting that further generalizations are in store.