University of Isfahan International Journal of Group Theory 2251-7650 14 2 2023 12 16 A generalization of the Chermak--Delgado measure on subgroups and its associated lattice 75 91 28020 10.22108/ijgt.2023.138469.1859 EN William Cocke School of Computer and Cyber Sciences, Augusta University, 100 Grace Hopper Ln, Augusta, GA 30901, USA Luise-Charlotte Kappe Department of Mathematics and Statistics, Binghamton University, P.O. Box 6000, Binghamton, NY 13902-6000, USA Arturo Magidin Department of Mathematics, University of Louisiana at Lafayette, P.O. Box 43568, Lafayette LA 70504-3568 USA Journal Article 2023 07 20 We generalize the Chermak--Delgado measure of a subgroup of a finite group $G$, $\mu(H) = |H||C_{G}(H)|$, and its associated lattice of subgroups with maximal measure. We consider mappings $M$ of the lattice of all subgroups $\mathrm{Sub}(G)$ into itself and define a measure associated to $M$ by setting $\mu(H)=|H||M(H)|$. We investigate under what conditions on $M$ the subgroups with maximal measure form a sublattice of $\mathrm{Sub}(G)$. In particular, our focus is on the case where $M(H)$ is a centralizer-like subgroup. https://ijgt.ui.ac.ir/article_28020_2cf9977be55d3a3fb6b0299966dee9c7.pdf