The lattice of closure operators on a subgroup lattice

Abstract

ABSTRACTWe 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 closure operators which act on the subgroup lattice of a finite group G is itself a subgroup lattice if and only if G is cyclic of prime power order.