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

2018/01/20 by Ryan McCulloch, Marius Tărnăuceanu · 2 citations
Mathematics · #math.GR

paper · pdf · doi:10.1080/00927872.2017.1404090

8 pages; accepted for publication in Comm. Algebra

arxiv created 2018/01/20 · arxiv updated 2018/01/23

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 \AC_B(A)\, a strengthening of earlier known results.

Cited by

• Finite groups with few subgroups not in the Chermak-Delgado lattice
• Finite groups with the most Chermak-Delgado measures of subgroups