Abstract:
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.
Key words:formation, Fitting class, $n$-multiply $\omega$-local formation, $n$-multiply $\omega$-local Fitting class, lattice of formations, product of formations, product of Fitting classes, maximal subformation.
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