Geodesic
On finite groups with semisubnormal residuals of Sylow normalizers
Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 58-62

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Let $\pi$ be some set of primes, $G$ be a $\pi$-soluble group and $G\in\mathfrak{E}_\pi\mathfrak{E}_{\pi'}$. It is proved that if for any prime $p\in\pi\cap\pi(G)$ and Sylow $p$-subgroup $P$ from $G$ the normalizer $N_G(P)$ is $\pi$-supersoluble and its nilpotent residual is semisubnormal in $G$, then $G$ is $\pi$-supersoluble.
Keywords: finite group, Sylow normalizer, semisubnormal subgroup, nilpotent residual, $\pi$-supersoluble group. 
@article{PFMT_2022_2_a9,
     author = {A. F. Vasil'ev},
     title = {On finite groups with semisubnormal residuals of {Sylow} normalizers},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {58--62},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2022_2_a9/}
}
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A. F. Vasil'ev. On finite groups with semisubnormal residuals of Sylow normalizers. Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 58-62. http://geodesic.mathdoc.fr/item/PFMT_2022_2_a9/