A generalization of the Chermak–Delgado theorem to compact groups

We change Chermak–Delgado measure slightly so that it can be used for compact groups as well. Corresponding to this new measure, a lattice of open subgroups is obtained. Then we prove that if this lattice is non-empty in a compact group [Formula: see text], then [Formula: see text] has a characteristic open abelian subgroup [Formula: see text] such that [Formula: see text] for every abelian subgroup [Formula: see text]. This is a generalization of the well-known Chermak–Delgado Theorem.