Ben Brewster, Peter Hauck, Elizabeth Wilcox
October 2, 2013

### Abstract

Abstract. For a finite group G with subgroup H , the Chermak–Delgado measure of H in G refers to |H||CG(H)|${\vert H \vert \,\vert C_G(H) \vert }$. The set of all subgroups with maximal Chermak–Delgado measure form a sublattice, 𝒞𝒟(G)$\mathcal {CD}(G)$, within the subgroup lattice of G . This paper examines conditions under which the Chermak–Delgado lattice is a chain of subgroups H0<H1<⋯<Hn${H_0 < H_1 < \cdots < H_n}$. On the basis of a general result about extending certain Chermak–Delgado lattices, we construct, for any prime p and any non-negative integer n , a p -group whose Chermak–Delgado lattice is a chain of length n .