Geodesic
Multiply $\omega$-Local Formations and Fitting Classes of Finite Groups
Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 114-147

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The present article deals only with finite groups. Functions of the form $$ f\colon\omega\cup\{\omega'\}\to\{\text{group formations}\} $$ are called $\omega$-local satellites (here $\omega$ denotes a nonempty set of primes). Functions of this form are used to study the structure of the $\omega$-local formations, i.e. the formations $\mathfrak{F}$ such that $G\in\mathfrak{F}$ whenever $G/\Phi(G)\cap O_{\omega}(G)\in\mathfrak{F}$. The theory of $\omega$-local Fitting classes is analyzed which is dual to the theory of $\omega$-local formations. 
@article{MT_1999_2_2_a6,
     author = {A. N. Skiba and L. A. Shemetkov},
     title = {Multiply $\omega${-Local} {Formations} and {Fitting} {Classes} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {114--147},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_1999_2_2_a6/}
}
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A. N. Skiba; L. A. Shemetkov. Multiply $\omega$-Local Formations and Fitting Classes of Finite Groups. Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 114-147. http://geodesic.mathdoc.fr/item/MT_1999_2_2_a6/