Geodesic
Finite Groups with Hereditarily $G$-Permutable Minimal Subgroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 102-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, the structure of a finite group $G$ all of whose minimal subgroups are hereditarily $G$-permutable is studied.
Keywords: finite group, minimal subgroup, $G$-permutable subgroup, hereditarily $G$-permutable subgroup, supersoluble group
Mots-clés : soluble group. 
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S. F. Kamornikov; V. N. Tyutyanov. Finite Groups with Hereditarily $G$-Permutable Minimal Subgroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 102-110. http://geodesic.mathdoc.fr/item/TIMM_2023_29_1_a7/

[1] Guo W., Shum K.P., Skiba A.N., “$X$-quasinormal subgroups”, Sib. Math. J., 48 (2007), 593–605 | DOI | MR | Zbl

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

[3] Ore O., “Contributions in the theory of groups of finite order”, Duke Math. J., 5 (1939), 431–460 | DOI | MR | Zbl

[4] Itô N., Szép J., “Über die Quasinormalteiler von endlichen Gruppen”, Act. Sci. Math., 23:1–2 (1962), 168–170 | MR | Zbl

[5] Huppert B., Endliche Gruppen I, Springer-Verlag, Berlin, 1967, 796 pp. | DOI | MR | Zbl

[6] Buckley J., “Finite groups whose minimal subgroups are normal”, Math. Z., 116 (1970), 15–17 | DOI | MR | Zbl

[7] Al-Shomrani M.M., Ramadan M., Heliel A.A., “Finite groups whose minimal subgroups are weakly $H$-subgroups”, Acta Math. Sci., 32:6 (2012), 2295–2301 | DOI | MR | Zbl

[8] Thompson J.G., “Nonsolvable finite groups all of whose local subgroups are solvable”, Bull. Amer. Math. Soc., 74:3 (1968), 383–437 | DOI | MR | Zbl

[9] Galt A.A., Tyutyanov V.N., “On the existence of $G$-permutable subgroups in simple sporadic groups ”, Sib. Math. J., 63:4 (2022), 691–698 | DOI | MR

[10] Ito N., “On the factorizations of the linear fractional groups $LF(2, p^n)$”, Acta Scient. Math., 15 (1953), 79–84 | MR | Zbl

[11] Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A., Atlas of finite groups, Oxford Univ. Press, Oxford, 1985, 252 pp. | DOI | MR | Zbl

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

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

[14] Shemetkov L.A., Formatsii konechnykh grupp, Nauka, Moskva, 1978, 271 pp. | MR

[15] Kantor W.M., Seress A., “Prime power graphs for groups of Lie type”, J. Algebra, 247 (2002), 370–343 | DOI | MR