Geodesic
On the $p$-length of a finite factorizable group with given permutability conditions for subgroups of factors
Problemy fiziki, matematiki i tehniki, no. 3 (2023), pp. 44-47

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A subgroup $A$ of a group $G$ is called $tcc$-subgroup in $G$, if there is a subgroup $T$ of $G$ such that $G=AT$ and for any $X\leq A$ and for any $Y\leq T$ there exists an element $u\in\langle X, Y\rangle$ such that $XY^u\leqslant G$. Suppose that $G=AB$ is a product of two $p$-soluble $tcc$-subgroups $A$ and $B$. We give a bound of the $p$-length of $G$ from the nilpotent class and the number of generators of $A_p$ and $B_p$, where $A_p$ and $B_p$ are the Sylow subgroups of $A$ and $B$ respectively.
Keywords: finite group, $tcc$-subgroup, $p$-length.
Mots-clés : $p$-solvable group 
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     author = {E. V. Zubei and A. A. Trofimuk},
     title = {On the $p$-length of a finite factorizable group with given permutability conditions for subgroups of factors},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {44--47},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2023_3_a7/}
}
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E. V. Zubei; A. A. Trofimuk. On the $p$-length of a finite factorizable group with given permutability conditions for subgroups of factors. Problemy fiziki, matematiki i tehniki, no. 3 (2023), pp. 44-47. http://geodesic.mathdoc.fr/item/PFMT_2023_3_a7/