Realization theorems for valuated \(p^n\)-socles.
The author and colleagues have previously proved that \(n\)-summable valuated \(p^n\)-socles are isometric if and only if their Ulm functions agree. In this paper, he poses and answers three related questions:{\parindent=5mm\begin{itemize} \item[1)] Which cardinal valued functions on countable ordinals are Ulm functions of some \(n\)-summable valuated \(p^n\)-socle?\item [2)] Which \(n\)-summable valuated \(p^n\)-socles are realizable as the \(p^n\)-socles of some Abelian \(p\)-group?\item [3)] Which \(n\)-summable Abelian \(p\)-groups are determined by their Ulm functions? \end{itemize}}
scientific article; zbMATH DE number 6005075