Geodesic
Satellites and products of $\Omega\zeta$-foliated Fitting classes
Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 2, pp. 152-161.

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All groups are assumed to be finite. Fitting class $\frak F=\Omega\zeta R(f,\varphi )=(G: O^\Omega (G)\in f(\Omega' )$ and $G^{\varphi (\Omega\cap\zeta_i )}\in f(\Omega\cap\zeta_i )$ for all $\Omega\cap\zeta_i \in\Omega\zeta (G))$ is called the $\Omega\zeta$-foliated Fitting class with $\Omega\zeta$-satellite $f$ and $\Omega\zeta$-direction $\varphi $. The directions of the $\Omega\zeta$-free and $\Omega\zeta$-canonical Fitting classes are denoted by $\varphi_0 $ and $\varphi_1 $, respectively. The paper describes the minimal $\Omega\zeta$-satellite of the $\Omega\zeta$-foliated Fitting class with $\Omega\zeta$-direction $\varphi$, where $\varphi_0\le\varphi $. It is shown that the Fitting product of two $\Omega\zeta$-foliated Fitting classes is $\Omega\zeta$-foliated Fitting class for $\Omega\zeta$-directions $\varphi$ such that $\varphi_0\le\varphi\le\varphi_1$. For $\Omega\zeta$-free and $\Omega\zeta$-canonical Fitting classes, results are obtained as corollaries of theorems. A maximal inner $\Omega\zeta$-satellite of an $\Omega\zeta$-free Fitting class and a maximal inner $\Omega\zeta\mathcal L$-satellite of the $\Omega\zeta$-canonical Fitting class are described. The results obtained can be used to study lattices, further study products and critical $\Omega\zeta$-foliated Fitting classes.
Keywords: finite group, Fitting class, $\Omega\zeta$-foliated, $\Omega\zeta$-free, $\Omega\zeta$-canonical, minimal $\Omega\zeta$-satellite, maximal internal $\Omega\zeta$-satellite, Fitting product. 
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O. V. Kamozina. Satellites and products of $\Omega\zeta$-foliated Fitting classes. Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 2, pp. 152-161. http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_2_a1/

[1] Skachkova Yu.A., “Lattices of $\Omega$-foliated formations”, Discrete Mathematics and Applications, 12:3 (2002), 269–278 | DOI | MR | Zbl

[2] Elovikov A.B., “he factorisation of one-generated partially foliated formations”, Discrete Mathematics and Applications, 19:4 (2009), 411–430 | DOI | MR | Zbl

[3] Vedernikov V.A., Egorova V.E., “Critical totally $\Omega$-canonical formations of finite groups”, News of F. Skorina Gomel State University, 2006, no. 3 (36), 8–13 (In Russ.)

[4] Egorova V.E., “Critical non-singly-generated totally canonical Fitting classes of finite groups”, Mathematical Notes, 83:4 (2008), 478–484 | DOI | MR | Zbl

[5] Kamozina O.V., “$\Omega\zeta$-foliated Fitting classes”, News of Saratov University. New Series. Series Mathematics. Mechanics. Informatics, 20:4 (2020), 424–433 | DOI | MR | Zbl

[6] Skiba A. N., “On one generalization of the local formations”, Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2018, no. 1 (34), 79–82 | MR | Zbl

[7] Skiba A.N., Shemetkov L.A., “Multiply $\omega$-local formations and Fitting classes of finite groups”, Siberian Advances in Mathematics, 10:2 (2000), 112–141 | MR | MR | Zbl | Zbl

[8] Doerk K., Nawkes T., Finite soluble groups, Walter de Gruyter, Berlin; New York, 1992 | MR

[9] Vedernikov V.A., Sorokina M.M., “$\Omega$-foliated formations and Fitting classes of finite groups”, Discrete Mathematics and Applications, 11:5 (2001), 507–527 | DOI | MR | Zbl

[10] Vedernikov V.A., “On new types of $\omega$-fibered Fitting classes of finite groups”, Ukrainian Mathematical Journal, 54:7 (2002), 1086–1097 | DOI | MR | Zbl