On complements of coradicals of finite groups

V. A. Vedernikov   ; M. M. Sorokina

Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 792-815

Résumé

Let $\mathfrak F$ be an $\omega$-local Fitting formation, and $G$ a finite group that can be represented in the form of a product of $n$ subnormal subgroups whose $\mathfrak F$-coradicals are $\omega$-soluble, and whose Sylow $p$-subgroups are abelian for any $p\in\omega$. It is established that there exist $\omega$-complements of the $\mathfrak F$-coradical of $G$. New theorems on the existence of complements of coradicals of a group are obtained as corollaries. For an $\omega$-local formation $\mathfrak F$, conditions are established for the existence of complements and $\omega$-complements of the $\mathfrak F$-coradical of a group in any of its extensions. Bibliography: 21 titles.

Détail

Keywords: finite group, Fitting class, $\omega$-local formation, coradical of a group, $\omega$-complement of a subgroup.

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