Geodesic
Injectors in Fitting Sets of Finite Groups
Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 516-528

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A set of subgroups $\mathscr F$ of a finite group $G$ is referred to as a Fitting set if it is closed with respect to taking normal subgroups, products of normal $\mathscr F$-subgroups, and inner automorphisms of $G$. A Fitting set $\mathscr F$ of a group $G$ is said to be $\pi$-saturated if $H\in\mathscr F$ for every subgroup $H$ in $G$ such that $O^{\pi'}(H)\in\mathscr F$. In the paper, it is proved that, if $\mathscr F$ is a $\pi$-saturated Fitting set of a $\pi$-solvable group $G$, then there are $\mathscr F$-injectors in $G$ and every two of them are conjugate.
Keywords: finite group, Fitting set, $\pi$-saturated Fitting set.
Mots-clés : $\pi$-solvable group 
@article{MZM_2015_97_4_a3,
     author = {N. T. Vorob'ev and M. G. Semenov},
     title = {Injectors in {Fitting} {Sets} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {516--528},
     publisher = {mathdoc},
     volume = {97},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a3/}
}
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N. T. Vorob'ev; M. G. Semenov. Injectors in Fitting Sets of Finite Groups. Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 516-528. http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a3/