Geodesic
Finite groups with weakly subnormal Schmidt subgroups
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 50-57

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A non-nilpotent finite group whose all proper subgroups are nilpotent is called a Schmidt group. A subgroup $H$ of a group $G$ is called weakly subnormal in $G$ if $H$ is generated by two subgroups, one of which is subnormal in $G$ and the other is seminormal in $G$. We establish $3$-solvability of a finite group with weakly subnormal $\{2,3\}$-Schmidt subgroups. This implies solvability of a finite group with weakly subnormal $\{2,3\}$-Schmidt subgroups and $5$-closed $\{2,5\}$-Schmidt subgroups. We prove nilpotency of the derived subgroup of a finite group in which all Schmidt subgroups are weakly subnormal. 
@article{TIMB_2023_31_1_a6,
     author = {V. N. Kniahina and V. S. Monakhov},
     title = {Finite groups with weakly subnormal {Schmidt} subgroups},
     journal = {Trudy Instituta matematiki},
     pages = {50--57},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a6/}
}
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V. N. Kniahina; V. S. Monakhov. Finite groups with weakly subnormal Schmidt subgroups. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 50-57. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a6/