Geodesic
Three Formations over~$\mathfrak U$
Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 358-367.

Voir la notice de l'article provenant de la source Math-Net.Ru

Three classes of finite groups are investigated in which all metanilpotent subgroups, all subgroups with nilpotent derived subgroup, or all Schmidt subgroups are supersolvable.
Keywords: finite group, Schmidt group, $\mathbb P$-subnormal subgroup.
Mots-clés : formation, supersolvable group 
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V. S. Monakhov. Three Formations over~$\mathfrak U$. Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 358-367. http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a3/

[1] B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin, 1967 | MR

[2] L. S. Kazarin, “O gruppakh s faktorizatsiei”, Dokl. AN SSSR, 256:1 (1981), 26–29 | MR | Zbl

[3] A. F. Vasilev, T. I. Vasileva, V. N. Tyutyanov, “O konechnykh gruppakh sverkhrazreshimogo tipa”, Sib. matem. zhurn., 51:6 (2010), 1270–1281 | MR

[4] V. S. Monakhov, “Konechnye gruppy s abnormalnymi i $\mathfrak U$-subnormalnymi podgruppami”, Sib. matem. zhurn., 57:2 (2016), 447–462 | DOI | MR

[5] V. S. Monakhov, “O konechnykh gruppakh s zadannym naborom podgrupp Shmidta”, Matem. zametki, 58:5 (1995), 717–722 | MR | Zbl

[6] O. Yu. Shmidt, “Gruppy, vse podgruppy kotorykh spetsialnye”, Matem. sb., 31:3-4 (1924), 366–372 | Zbl

[7] L. A. Shemetkov, Formatsii konechnykh grupp. Sovremennaya algebra, Nauka, M., 1978 | MR

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

[9] K. Doerk, “Minimal nicht überauflösbare, endliche Gruppen”, Math. Z., 91 (1966), 198–205 | DOI | MR

[10] V. T. Nagrebetskii, “O konechnykh minimalnykh nesverkhrazreshimykh gruppakh”, Konechnye gruppy, Nauka i tekhnika, Minsk, 1975, 104–108

[11] The GAP Group: GAP – Groups, Algorithms, and Programming, Ver. 4.11.0 released on 29 February 2020, www.gap-system.org

[12] J. C. Beidleman, H. Heineken, “Minimal non-$\mathfrak F$-groups”, Ric. Mat., 58:1 (2009), 33–41 | DOI | MR

[13] V. N. Tyutyanov, P. V. Bychkov, “O konechnykh gruppakh s minimalnymi $\mathbb{P}$-subnormalnymi podgruppami”, PFMT, 2014, no. 4 (21), 97–99

[14] V. P. Burichenko, “O gruppakh, elementy malykh poryadkov kotorykh porozhdayut maluyu podgruppu”, Matem. zametki, 92:3 (2012), 361–367 | DOI | MR | Zbl

[15] P. J. Cameron, R. Solomon, A. Turull, “Chains of subgroups in symmetric groups”, J. Algebra, 127:2 (1989), 340–352 | DOI | MR

[16] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups, Clarendon, London, 1985 | MR