Geodesic
On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups
Trudy Instituta matematiki, Tome 24 (2016) no. 1, pp. 34-37

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A Schmidt group is a finite nonnilpotent group in which every proper subgroup is nilpotent. Fix a positive integer $n.$ Let $G$ be a solvable group. Suppose that each $n$-maximal subgroup of $G$ is permutable with every $p$-nilpotent Schmidt subgroup. We prove that if $n\in\{1,2,3\},$ then $G/F(G)$ is $p$-closed, where $F(G)$ is the Fitting subgroup of $G$. 
@article{TIMB_2016_24_1_a4,
     author = {V. N. Kniahina},
     title = {On permutability of $n$-maximal subgroups with $p$-nilpotent {Schmidt} subgroups},
     journal = {Trudy Instituta matematiki},
     pages = {34--37},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a4/}
}
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V. N. Kniahina. On permutability of $n$-maximal subgroups with $p$-nilpotent Schmidt subgroups. Trudy Instituta matematiki, Tome 24 (2016) no. 1, pp. 34-37. http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a4/