Geodesic
Finite groups with hereditarily $G$-permutable subgroups of small order
Problemy fiziki, matematiki i tehniki, no. 1 (2024), pp. 63-67.

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The structure of a finite group $G$ is investigated, in which all subgroups of order 2 and 3 as well as all cyclic subgroups of order 4 are hereditarily $G$-permutable in $G$.
Keywords: finite group, hereditarily $G$-permutable subgroup
Mots-clés : soluble group. 
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P. V. Bychkov; S. F. Kamornikov; V. N. Tyutyanov. Finite groups with hereditarily $G$-permutable subgroups of small order. Problemy fiziki, matematiki i tehniki, no. 1 (2024), pp. 63-67. http://geodesic.mathdoc.fr/item/PFMT_2024_1_a8/

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

[2] V. Go, A.N. Skiba, K.P. Sham, “X-perestanovochnye podgruppy”, Sibirskii matematicheskii zhurnal, 48:4 (2007), 742–759 | Zbl

[3] A.A. Galt, V.N. Tyutyanov, “O suschestvovanii G-perestanovochnykh podgrupp v prostykh sporadicheskikh gruppakh”, Sibirskii matematicheskii zhurnal, 63:4 (2022), 831–841

[4] A.A. Galt, V.N. Tyutyanov, “O suschestvovanii G-perestanovochnykh podgrupp v isklyuchitelnykh gruppakh G lieva tipa”, Sibirskii matematicheskii zhurnal, 64:5 (2023), 935–945 | Zbl

[5] S.F. Kamornikov, V.N. Tyutyanov, “Konechnye gruppy s nasledstvenno G-perestanovochnymi minimalnymi podgruppami”, Trudy Instituta matematiki i mekhaniki UrO RAN, 29, no. 1, 2023, 102–110 | Zbl

[6] S.F. Kamornikov, V.N. Tyutyanov, “O razreshimosti i sverkhrazreshimosti konechnykh grupp”, Sibirskii matematicheskii zhurnal, 64:2 (2023), 312–320 | Zbl

[7] A. Ballester-Bolinches, S.F. Kamornikov, V. Pérez-Calabuig, V.N. Tyutyanov, “Finite groups with G-permutable Schmidt subgroups”, Mediterranean Journal of Mathematics, 20 (2023), 174, 12 pp. | DOI | MR | Zbl

[8] A. Ballester-Bolinches, S.F. Kamornikov, V. Pérez-Calabuig, V.N. Tyutyanov, “Finite groups with hereditarily G-permutable Schmidt subgroups”, Bull. Austral. Math. Soc., 2023, 1–7 | DOI | MR

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

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

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

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

[13] D. Gorenstein, Finite groups, American Mathematical Society, New York, 1980, 519 pp. | MR

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

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

[16] L.A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp.