A generalization of the Chermak-Delgado theorem to compact groups

Abstract

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 G, then G has a characteristic open abelian subgroup N such that [G: N] ≤ [G: A]2 for every abelian subgroup A G. This is a generalization of the well-known Chermak-Delgado Theorem. © 2026 World Scientific Publishing Company.