Finite groups with large Chermak-Delgado lattices

Abstract

Given a finite group $G$, we denote by $L(G)$ the subgroup lattice of $G$ and by $\mathcal{C}\mathcal{D}(G)$ the Chermak-Delgado lattice of $G$. In this note, we determine the finite groups $G$ such that $|\mathcal{C}\mathcal{D}(G)|=|L(G)|-k$, $k=1,2$.

References in corpus (1)

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