A Functorial Generalization of the Fitting Subgroup in Finite Groups

Using the functional approach of R. Baer and B. I. Plotkin, we introduce and study the notion of ℱ-functorial whose values are characteristic subgroups of a finite group that possess certain properties of the Fitting subgroup. The lattice and semigroups of ℱ-functorials are described, the interrelation between ℱ-functorials and classes of groups is established, a characterization of their values is given in terms of group’s elements inducing inner automorphisms on specified chief factors.