Geodesic
A functorial generalization of the Fitting subgroup in finite groups
Algebra i logika, Tome 62 (2023) no. 5, pp. 593-613.

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Using the functional approach of R. Baer and B. I. Plotkin, we introduce and study the notion of $\mathcal{F}$-functorial whose values are characteristic subgroups of a finite group that possess certain properties of the Fitting subgroup. The lattice and semigroups of $\mathcal{F}$-functorials are described, the interrelation between $\mathcal{F}$-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.
Keywords: finite group, Fitting subgroup, generalized Fitting subgroup, functorial, Plotkin radical. 
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V. I. Murashko; A. F. Vasil'ev. A functorial generalization of the Fitting subgroup in finite groups. Algebra i logika, Tome 62 (2023) no. 5, pp. 593-613. http://geodesic.mathdoc.fr/item/AL_2023_62_5_a1/

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