Abelian p-groups with a fixed elementary subgroup or with a fixed elementary quotient

Justyna Kosakowska, Markus Schmidmeier, Martin Schreiner

In his 1934 paper, G.\ Birkhoff poses the problem of classifying pairs $(G,U)$ where $G$ is an abelian group and $U\subset G$ a subgroup, up to automorphisms of $G$. In general, Bi…