Groups whose Chermak–Delgado lattice is a subgroup lattice of an abelian group

Abstract The Chermak–Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G . In this paper, we prove that, for any finite abelian group A , there exists a finite group G such that the Chermak–Delgado lattice of G is a subgroup lattice of A .