Geodesic
A criterion for the σ-subnormality of a subgroup in a finite 3′-group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 36-43.

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For a partition σ of the set P of all primes, it is solved, that if a subgroup H of a finite 3′-group G is σ-subnormal in $$ for any x∈G, then H is σ-subnormal in G.
Mots-clés : finite group, σ-subnormal subgroup, subnormal subgroup, Suzuki group. 
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S. F. Kamornikov; V. N. Tyutyanov. A criterion for the $\sigma$-subnormality of a subgroup in a finite $3'$-group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 36-43. https://geodesic-test.mathdoc.fr/item/IVM_2020_8_a3/

[1] Wielandt H., “Kriterien für Subnormalität in endlichen Gruppen”, Math. Z., 138:3 (1974), 199–203 | DOI | MR | Zbl

[2] The Kourovka notebook. Unsolved problems in group theory, Sobolev Inst. Math., Sib. Branch Russian Acad. of Sci.,, Novosibirsk, 2018

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

[4] Wielandt H., “Eine Verallgemeinerung der invarianten Untergruppen”, Math. Z., 45 (1939), 209–244 | MR

[5] Skiba A. N., “On $\sigma$-subnormal and $\sigma$-permutable subgroups of finite groups”, J. Algebra, 436 (2015), 1–16 | DOI | MR | Zbl

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

[7] Ballester-Bolinches A., Ezquerro L. M., Classes of finite groups, Springer, New York, 2006 | MR | Zbl

[8] Kegel O. H., “Untergruppenverbände endlicher Gruppen, die den Subnormalteilerverband echt enthalten”, Arch. Math., 30:3 (1978), 225–228 | MR | Zbl

[9] Kamornikov S. F., “Permutability of subgroups and $\mathfrak F$-subnormality”, Sib. Math. J., 37:5 (1996), 936–949 | MR | Zbl

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

[11] Guest S., “A solvable version of the Baer-Suzuki theorem”, Trans. Amer. Math. Soc., 362 (2010), 5909–5949 | DOI | MR

[12] Gorenstein D., Lyons R., “The local structure of the finite groups of characteristic $2$ type”, Memoirs AMS, 42, no. 276, 1983, 1–731 | DOI | MR