On complements of coradicals of finite groups
Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 792-815
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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.
Keywords:
finite group, Fitting class, $\omega$-local formation, coradical of a group, $\omega$-complement of a subgroup.
@article{SM_2016_207_6_a1,
author = {V. A. Vedernikov and M. M. Sorokina},
title = {On complements of coradicals of finite groups},
journal = {Sbornik. Mathematics},
pages = {792--815},
publisher = {mathdoc},
volume = {207},
number = {6},
year = {2016},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2016_207_6_a1/}
}
V. A. Vedernikov; M. M. Sorokina. On complements of coradicals of finite groups. Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 792-815. http://geodesic.mathdoc.fr/item/SM_2016_207_6_a1/