A generalization of the Chermak--Delgado measure on subgroups and its associated lattice

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.

کلیدواژه ها:

subgroup lattice ، characteristic subgroup ، Chermak-Delgado lattice ، CD-admissible function