A generalization of the Chermak--Delgado measure on subgroups and its associated lattice
نویسندگان
1 Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
2 Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
3 Department of Geometry and Algebra, Oles Honchar Dnipro National University Departament de Matemàtiques, Universitat de València
4 Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100, Burjassot, València, Spain
doi
10.22108/ijgt.2023.138469.1859چکیده
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.
