Geodesic
On the $\mathrm{w}$-supersolubility of a finite group factorized by mutually permutable subgroups
Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 238-244

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The subgroups $A$ and $B$ of a group $G$ are called mutually permutable if $A$ permutes with all subgroups of $B$ and $B$ permutes with all subgroups of $A$. The sufficient conditions of $\mathrm{w}$-supersolubility of a group $G = AB$ that is factorized by two mutually permutable $\mathrm{w}$-supersoluble subgroups $A$ and $B$ were obtained. Besides we found the construction of $\mathrm{w}$-supersoluble residual of such group.
Keywords: finite group, $\mathrm{w}$-supersoluble group, mutually permutable subgroups, $\mathfrak F$-residual. 
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     title = {On the $\mathrm{w}$-supersolubility of a finite group factorized by mutually permutable subgroups},
     journal = {\v{C}eby\v{s}evskij sbornik},
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N. V. Artemenko; A. A. Trofimuk. On the $\mathrm{w}$-supersolubility of a finite group factorized by mutually permutable subgroups. Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 238-244. http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a16/