A functorial generalization of the Fitting subgroup in finite groups (Q6633365)

Let \(G\) be a finite group. The authors, using the functional approach of \textit{R. Baer} [Colloq. Math. 14, 285--327 (1966; Zbl 0143.03804)] and \textit{B. I. Plotkin} [Transl., Ser. 2, Am. Math. Soc. 119, 89--118 (1983; Zbl 0502.20010)], introduce and study the notion of \(\mathfrak{F}\)-functorial whose values are characteristic subgroups of a finite group that possess certain properties of the Fitting subgroup. The lattice and semigroups of \(\mathfrak{F}\)-functorials are described, the interrelation between \(\mathfrak{F}\)-functorials and classes of groups is established and a characterization of their values is given in terms of the elements of the group inducing inner automorphisms on specified chief factors.