2024/01/23 by Cocke, William, McCulloch, Ryan · 1 citation
#20E15 #FOS: Mathematics #Group Theory (math.GR) #Primary 20D30
paper · doi:10.48550/arxiv.2401.12450
The Chermak-Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when the Chermak-Delgado measure of a group is actually a map of posets, i.e., a monotone function from the subgroup lattice to the positive integers. We also investigate when the Chermak-Delgado measure, restricted to the centralizers, is increasing.