Geodesic
Formula of an injector of a finite $\pi$-soluble group
Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 77-88

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Let $G$ be a finite $\pi$-soluble group. We say that a Fitting set $\mathcal{F}$ of $G$ is $\pi$-saturated if it verifies $H\in\mathcal{F}$ whenever $O^{\pi'}(H)\in\mathcal{F}$. It is proved that $\mathcal{F}$-injector of $G$ is a subgroup of the form $W\cdot C_{D_p}(W/W_{F(p)})$, where $\mathcal{F}$ is a $\pi$-saturated Fitting set, which is defined with full integrated $H$-function $F$ of $G$, $\Sigma$ — Hall system of $G$, $D=N_G(\Sigma)$, $p\in\pi(G)\cap\pi\ne\varnothing$, $D_p\in\Sigma\cap D$, $W$ is an $\mathcal{F}$-injector of $O^p(G)$ and $\Sigma\searrow W$.
Keywords: finite $\pi$-soluble group, $\pi$-saturated Fitting set, $\mathcal{F}$-injector. 
@article{PFMT_2014_4_a11,
     author = {M. G. Semenov},
     title = {Formula of an injector of a finite $\pi$-soluble group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {77--88},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_4_a11/}
}
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M. G. Semenov. Formula of an injector of a finite $\pi$-soluble group. Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 77-88. http://geodesic.mathdoc.fr/item/PFMT_2014_4_a11/