Satellites and products of $\Omega\zeta$-foliated Fitting classes

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.