On variations of \(m,n\)-simply presented Abelian \(p\)-groups. (Q477245)

This paper concerns generalizations of well known properties of infinite abelian \(p\)-groups, for example simply-presented or \(p^\lambda\)-projective. For a given property \(P\), a group \(G\) is called an \(n\)-\(P\)-group if \(G\) has a \(p^n\)-bounded subgroup \(H\) such that \(G/H\) is a \(P\)-group; and \(G\) is an \(m,n\)-\(P\)-group if there exists an \(m\)-\(P\)-group \(H\) containing a \(p^n\)-bounded subgroup \(K\) such that \(G=H/K\). The paper contains a host of variations of these definitions and considers the relations among these properties as \(m,n\) and \(P\) vary. The author considers also the inheritance of the properties under the operations \(G\to p^\lambda G\) and \(G\to G/p^\lambda G\) for various ordinals \(\lambda\). He exhaustively settles these problems or poses them as Conjectures or Questions.