The Kegel--Wielandt $\sigma$-problem for the partition $\sigma= \{\{2\},\{3\},\{2,3\}'\}$
Problemy fiziki, matematiki i tehniki, no. 4 (2023), pp. 64-68.

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For the partition $\sigma= \{\{2\},\{3\},\{2,3\}'\}$ of the set of all primes, the Kegel–Wielandt $\sigma$-problem is solved.
Keywords: finite group, Hall subgroup, $\sigma$-subnormal subgroup, Kegel–Wielandt $\sigma$-problem.
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S. F. Kamornikov; V. N. Tyutyanov. The Kegel--Wielandt $\sigma$-problem for the partition $\sigma= \{\{2\},\{3\},\{2,3\}'\}$. Problemy fiziki, matematiki i tehniki, no. 4 (2023), pp. 64-68. http://geodesic.mathdoc.fr/item/PFMT_2023_4_a10/

[1] O.H. Kegel, “Sylow-Gruppen und Subnormalteiler endlicher Gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[2] H. Wielandt, “Zusammengesetzte Gruppen: Holders Programm heute”, Proc. Pure Math., 37 (1980), 161–173 | DOI | MR | Zbl

[3] P.B. Kleidman, “A proof of the Kegel–Wielandt conjecture on subnormal subgroups”, Ann. Math., 133 (1991), 369–428 | DOI | MR | Zbl

[4] The Kourovka Notebook: Unsolved problems in group theory, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2022, 269 pp.

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

[6] A. Ballester-Bolinches, S.F. Kamornikov, V.N. Tyutyanov, “On the Kegel-Wielandt $\sigma$-problem for binary partitions”, Annali di Matematica Pura ed Applicata, 201 (2022), 443–451 | DOI | MR

[7] R. Guralnick, P.B. Kleidman, R. Lyons, “Sylow $p$-subgroups and subnormal subgroups of finite groups”, Proc. London Math. Soc., 66:1 (1993), 129–151 | DOI | MR | Zbl

[8] C.Y. Li, X. Li, “On permutation groups of degree a product of two prime-powers”, Communications in Algebra, 42 (2014), 4722–4743 | DOI | MR | Zbl

[9] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 891 pp. | MR

[10] F. Gross, “Hall subgroups of order not divisible by 3”, Rocky mountain journal of mathematics, 23:2 (1993), 569–591 | DOI | MR | Zbl

[11] K. Zsigmondy, “Zur Theorie der Potenzreste”, Monath. Math. Phis., 3 (1892), 265–284 | DOI | MR

[12] P. Kleidman, M. Liebeck, The subgroup structure of the finite classical groups, Cambridge University Press, Cambridge, 1990, 303 pp. | MR | Zbl

[13] S.F. Kamornikov, V.N. Tyutyanov, “On $\sigma$-subnormal subgroups of finite groups”, Siberian Mathematical Journal, 61:2 (2020), 266–270 | DOI | MR | Zbl

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

[15] E.P. Vdovin, D.O. Revin, “Teoremy silovskogo tipa”, UMN, 66:5 (2011), 3–46 | DOI

[16] S.F. Kamornikov, V.N. Tyutyanov, “On some aspects of the Kegel-Wielandt $\sigma$-problem”, Russian Mathematics, 66:2 (2022), 15–24 | DOI | MR

[17] H.I. Blau, “On trivial intersection of cyclic Sylow subgroups”, Proc. Amer. Math. Soc., 94 (1985), 572–576 | DOI | MR | Zbl