Finite groups with $\mathbb{P}$-subnormal subgroups
Problemy fiziki, matematiki i tehniki, no. 1 (2016), pp. 68-70.

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The structure of finite group $G$, in which single subgroup is not $\mathbb{P}$-subnormal in $G$, but $\mathbb{P}$-subnormal in any proper subgroup of $G$, was established.
Keywords: finite group, composition factors, $\mathbb{P}$-subnormal subgroup.
Mots-clés : simple non-abelian group
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V. N. Tyutyanov; T. V. Tihonenko. Finite groups with $\mathbb{P}$-subnormal subgroups. Problemy fiziki, matematiki i tehniki, no. 1 (2016), pp. 68-70. http://geodesic.mathdoc.fr/item/PFMT_2016_1_a11/

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

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

[3] V. N. Kniahina, V. S. Monakhov, Finite groups with $\mathbb{P}$-subnormal primary cyclic subgroups, 21 Oct. 2011, 15 pp., arXiv: 1110.4720v1 [math.GR] | MR

[4] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp. | MR

[5] A. F. Vasilev, T. I. Vasileva, V. N. Tyutyanov, “O proizvedeniyakh $\mathbb{P}$-subnormalnykh podgrupp v konechnykh gruppakh”, Sib. mat. zhurnal, 53:1 (2012), 59–67 | MR | Zbl

[6] J. H. Conway et al., Atlas of finite groups, Oxford, 1985, 252 pp. | MR

[7] M. Suzuki, “On a class double transitive groups”, Ann. Math., 75:1 (1962), 105–145 | DOI | MR | Zbl

[8] P. Kleidman, “The maximal subgroups of the Chevalley groups $G_2(q)$ with $q$ odd, Ree groups $^2G_2(q)$ and their automorphism groups”, J. Algebra, 117 (1988), 30–71 | DOI | MR | Zbl

[9] B. Huppert, Endliche Gruppen, Springer, Berlin–Heidelberg–New York, 1967, 793 pp. | MR | Zbl

[10] H. H. Mitchell, “Determination of the ordinary and modular ternary linear groups”, Trans. Amer. Math. Soc., 12 (1911), 207–242 | DOI | MR | Zbl

[11] R. W. Hartley, “Determination of the ternary collineation groups whose coefficients lie in the $GF(2^n)$”, Ann. Math., 27 (1925), 140–158 | DOI | MR | Zbl

[12] E. Stensholt, “Certain embedding finite group of Lie type”, J. Algebra, 53 (1978), 136–187 | DOI | MR | Zbl