The lattice of algebraic closure operators on an infinite subgroup lattice
Martha L. H. Kilpack, Arturo Magidin · Communications in Algebra · 2021
We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)≅L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of algebraic closure operators which act on the subgroup lattice of an infinite group is itself a subgroup lattice if and only if the group is isomorphic to the Prüfer p-group.