Geodesic
On the permutability of Sylow subgroups with derived subgroups of $B$-subgroups
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 12-17

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A finite non-nilpotent group $G$ is called a $B$-group if every proper subgroup of the quotient group $G/\Phi(G)$ is nilpotent. We establish the $r$-solvability of the group in which some Sylow $r$-subgroup permutes with the derived subgroups of $2$-nilpotent (or $2$-closed) $B$-subgroups of even order and the solvability of the group in which the derived subgroups of $2$-closed and $2$-nilpotent $B$-subgroups of even order are permutable.
Keywords: finite group; $r$-solvable group; Sylow subgroup; $B$-group; the derived subgroup; permutable subgroups. 
@article{BGUMI_2019_1_a1,
     author = {E. V. Zubei},
     title = {On the permutability of {Sylow} subgroups with derived subgroups of $B$-subgroups},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {12--17},
     publisher = {mathdoc},
     volume = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2019_1_a1/}
}
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E. V. Zubei. On the permutability of Sylow subgroups with derived subgroups of $B$-subgroups. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 12-17. http://geodesic.mathdoc.fr/item/BGUMI_2019_1_a1/