Geodesic
On the permutability of $n$-maximal subgroups with Schmidt subgroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 125-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Schmidt group is a nonnilpotent group in which every proper subgroup is nilpotent. Let us fix a positive integer $n$ and assume that each $n$-maximal subgroup of a finite group $G$ is permutable with any Schmidt subgroup. We prove that, if $n\in\{1,2,3\}$, then $G$ is metanilpotent and, if $n\ge4$ and $G$ is solvable, then the nilpotent length of $G$ is at most $n-1$.
Keywords: finite group, Schmidt subgroup, nilpotent length.
Mots-clés : solvable group 
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V. N. Knyagina; V. S. Monakhov. On the permutability of $n$-maximal subgroups with Schmidt subgroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 125-130. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a14/

[1] Knyagina V. N., Monakhov V. S., “O perestanovochnosti maksimalnykh podgrupp s podgruppami Shmidta”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 126–133

[2] Huppert B., Endliche Gruppen, v. I, Springer-Verlag, Berlin–Heidelberg–New York, 1967, 793 pp. | MR | Zbl

[3] Monakhov V. S., “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Pratsi Ukrain. mat. kongresu-2001, Sekts. 1, In-t matematiki NAN Ukraini, Kiiv, 2002, 81–90 | MR | Zbl

[4] Knyagina V. N., Monakhov V. S., “Konechnye gruppy s polunormalnymi podgruppami Shmidta”, Algebra i logika, 46:4 (2007), 448–458 | MR | Zbl

[5] Lennox J. C., Stonehewer S. E., Subnormal subgroups of groups, Clarendon Press, Oxford, 1987, 253 pp. | MR | Zbl

[6] Gaschutz W., Lectures of subgroups of Sylow type in finite soluble groups, Notes on Pure Math., 11, Australian National University, Canberra, 1979, 100 pp. | MR

[7] Huppert B., “Normalteiler und maximale Untergruppen endlicher Gruppen”, Math. Z., 60:4 (1954), 409–434 | DOI | MR | Zbl