Two classes of finite groups whose Chermak-Delgado lattice is a chain of length zero

Abstract

It is an open question in the study of Chermak-Delgado lattices precisely which finite groups $G$ have the property that $CD(G)$ is a chain of length $0$. In this note, we determine two classes of groups with this property. We prove that if $G=AB$ is a finite group, where $A$ and $B$ are abelian subgroups of relatively prime orders with $A$ normal in $G$, then the Chermak-Delgado lattice of $G$ equals $\{A{C}_B(A)\}$, a strengthening of earlier known results.

8 pages; accepted for publication in Comm. Algebra

Cited by in corpus (1)

• Finite groups with large Chermak-Delgado lattices