Geodesic
Finite groups with some subnormal 2-maximal subgroups
Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 75-79.

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A finite group $G$ such that in every maximal subgroup of $G$ there is a subnormal in $G$ subgroup is studied. In particular, we proved that the derived subgroup of $G$ is nilpotent.
Keywords: finite group, subnormal subgroup, 2-maximal subgroup. 
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M. N. Konovalova; V. S. Monakhov. Finite groups with some subnormal 2-maximal subgroups. Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 75-79. http://geodesic.mathdoc.fr/item/PFMT_2020_2_a13/

[1] V.S. Monakhov, Vvedenie v teoriyu konechnykh grupp i ikh klassov, Vysheishaya shkola, Minsk, 2006, 207 pp.

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

[3] B. Huppert, “Normalteiler and maximal Untergruppen endlicher gruppen”, Math. Z., 60 (1954), 409–434 | MR | Zbl

[4] Yu.V. Lutsenko, A.N. Skiba, “Konechnye gruppy s subnormalnymi vtorymi ili tretimi maksimalnymi podgruppami”, Matem. zametki, 91:5 (2012), 730–740 | Zbl

[5] Yu.V. Gorbatova, M.N. Konovalova, “Konechnye gruppy s subnormalnymi strogo 2-maksimalnymi ili strogo 3-maksimalnymi podgruppami”, Vestnik Omskogo universiteta, 24:3 (2019), 4–11

[6] V.S. Monakhov, V.N. Kniahina, “Finite groups with $\mathbb{P}$-subnormal subgroups”, Ricerche Mat., 62 (2013), 307–322 | MR | Zbl

[7] V.A. Kovaleva, A.N. Skiba, “Finite soluble groups with all $n$-maximal subgroups $\mathfrak{F}$-subnormal”, J. Group Theory, 17:2 (2014), 273–290 | MR | Zbl

[8] V.S. Monakhov, “O gruppakh s formatsionno subnormalnymi 2-maksimalnymi podgruppami”, Matem. zametki, 105:2 (2019), 269–277 | Zbl

[9] W. Gaschütz, “Über die $\Phi$-Untergruppe endlicher Gruppen”, Math. Z., 58 (1953), 160–170 | MR | Zbl

[10] V.S. Monakhov, “Zamechaniya o maksimalnykh podgruppakh konechnykh grupp”, Doklady NAN Belarusi, 47:4 (2003), 31–33

[11] V.S. Monakhov, “Zamechanie o peresechenii nenormalnykh maksimalnykh podgruppakh konechnykh grupp”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2004, no. 6 (27), 81

[12] A.F. Vasilev, T.I. Vasileva, A.V. Syrokvashin, “Zametka o peresecheniyakh nekotorykh maksimalnykh podgrupp konechnykh grupp”, Problemy fiziki, matematiki i tekhniki, 2012, no. 2 (11), 62–64

[13] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 271 pp.

[14] M.I. Kargapolov, Yu.I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1982, 288 pp.

[15] V.S. Monakhov, “Podgruppy Shmidta, ikh suschestvovanie i nekotorye prilozheniya”, Trudy Ukr. matem. kongressa, sektsiya No 1 (2001, Kiev), 2002, 81–90

[16] A. Fattahi, “Groups with only normal and abnormal subgroups”, J. Algebra, 28:1 (1974), 15–19 | MR | Zbl

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

[18] A.N. Skiba, “On some results in the theory of finite partially soluble groups”, Commun. Math. Stat., 4:3 (2016), 281–309 | MR | Zbl

[19] V.I. Murashko, A.F. Vasilev, “O proizvedeniyakh chastichno subnormalnykh podgrupp konechnykh grupp”, Vesnik Vitsebskaga dzyarzhaŭnaga ŭniversiteta, 70:4 (2012), 24–27

[20] V.S. Monakhov, I.K. Chirik, “Konechnye gruppy, faktorizuemye subnormalnymi sverkhrazreshimymi podgruppami”, Problemy fiziki, matematiki i tekhniki, 2016, no. 3 (28), 40–46

[21] A.F. Vasilev, V.I. Murashko, “Formatsii i proizvedeniya $F(G)$-subnormalnykh podgrupp konechnykh razreshimykh grupp”, Matem. zametki, 107:3 (2020), 376–390 | Zbl