Geodesic
Injectors and Fischer subgroups of finite $\pi$-soluble groups
Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 70-75.

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Let $\mathscr{F}$ be a Fitting set of a group $G$ and $L\leq G$. Then $\mathscr{F}$ is called a Fischer set of $G$, if $L\in\mathscr{F}$, $K\unlhd L$ and $H/K$ is a $p$-subgroup of $L/K$ for some prime $p$, then $H\in\mathscr{F}$. A subgroup $F$ of a group $G$ is said to be Fischer $\mathscr{F}$-subgroup of $G$ if the following conditions are hold: (1) $F\in\mathscr{F}$; (2) if $F\leq H\leq G$, then $H_{\mathscr{F}}\leq F$. Let $\pi$ be some nonempty set of prime numbers. A Fitting set $\mathscr{F}$ of a group $G$ is said to be $\pi$-saturated if $\mathscr{F}=\{H\leq G: H/H_{\mathscr{F}}\in\mathfrak{E}_{\pi'}\}$, where $\mathfrak{E}_{\pi'}$ is the class of all $\pi'$-groups. In this paper it is proved that if $\mathscr{F}$ is a $\pi$-saturated Fischer set of a $\pi$-soluble group $G$, then a subgroup $V$ of a group $G$ is $\mathscr{F}$-injector of $G$ if and only if $V$ is a Fischer $\mathscr{F}$-subgroup of $G$, which contains Hall $\pi'$-subgroup of $G$.
Keywords: Fitting set, Fischer set, $\mathscr{F}$-injector, Fischer $\mathscr{F}$-subgroup of $G$. 
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     title = {Injectors and {Fischer} subgroups of finite $\pi$-soluble groups},
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     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_2_a9/}
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T. B. Karaulova. Injectors and Fischer subgroups of finite $\pi$-soluble groups. Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 70-75. http://geodesic.mathdoc.fr/item/PFMT_2019_2_a9/

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