Geodesic
On some product of $\mathrm{SM}$-groups
Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 170-175

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A subgroup $A$ of a group $G$ is called $\mathrm{tcc}$-subgroup in $G$, if there is a subgroup $T$ of $G$ such that $G=AT$ and for any $X\le A$ and $Y\le T$ there exists an element $u\in \langle X,Y\rangle $ such that $XY^u\leq G$. The notation $H\le G $ means that $H$ is a subgroup of a group $G$. In this paper we proved that the class of all $\mathrm{SM}$-groups is closed under the product of $\mathrm{tcc}$-subgroups. Here an $\mathrm{SM}$-group is a group where each subnormal subgroup permutes with every maximal subgroup.
Keywords: factorizable group, $\mathrm{tcc}$-subgroup, $\mathrm{SM}$-group. 
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     author = {D. V. Gritsuk and A. A. Trofimuk},
     title = {On some product of $\mathrm{SM}$-groups},
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     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_1_a12/}
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D. V. Gritsuk; A. A. Trofimuk. On some product of $\mathrm{SM}$-groups. Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 170-175. http://geodesic.mathdoc.fr/item/CHEB_2024_25_1_a12/