On generalizations of purity in primary Abelian groups (Q1330033)

All groups considered are abelian \(p\)-groups for a fixed prime \(p\). Fixing an ordinal \(\alpha\) the author investigates and answers the following three questions: (a) For which groups \(A\) is \(p^ \alpha\text{Ext}(A,B)\) always contained in \(\text{Bext}(A,B)\)? (b) For which groups \(A\) is \(\text{Bext}(A,B)\) always contained in \(p^ \alpha\text{Ext}(A,B)\)? (c) For which groups \(A\) is \(B^ \alpha\text{ext}(A,B) = p^ \alpha\text{Ext}(A,B) \cap \text{Bext}(A,B)\) always 0? The first two questions are treated in part 2, part 3 deals with the question (c) and presents several descriptions of the \(B^ \alpha\text{ext}\)-projectives.