Sharply doubly transitive groups with saturation conditions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 559-564.

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A number of conditions were found under which a sharply doubly transitive permutation group has an abelian normal divider.
Keywords: exactly doubly transitive group, Frobenius groups, finite and generalized finite the elements.
Mots-clés : saturation condition
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Anatoliy I. Sozutov; Evgeny B. Durakov. Sharply doubly transitive groups with saturation conditions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 559-564. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a1/

[1] C. Jordan, “Recherches sur les substitutions”, J. Math. Pures Appl., 17:2 (1872), 351–363

[2] Kourovka notebook: Unsolved problems of group theory, 6-17 ed., Novosibirsk, 1978–2012 | MR

[3] H. Wähling, Theorie der Fastkörper, Thalen Ferlag, Essen, 1987 | MR | Zbl

[4] E. Rips, Yo.Segev, K. Tent, A sharply 2-transitive group without a non-trivial abelian normal subgroup, 22 Oct. 2014, 17 pp., arXiv: 1406.0382v4 [math.GR] | MR

[5] K. Tent, M. Ziegler, “Sharply 2-transitive groups”, Advances in Geometry, 16 (2014), 1–5, arXiv: 1408.5612v1 [math.GR] | DOI | MR

[6] E. Rips, K. Tent, Sharply 2-transitive groups in characteristic 0, 2 Apr 2016, arXiv: 1604.00573 [math.GR] | MR

[7] S. Andre, K. Tent, Simple sharply 2-transitive groups, 18 Nov 2021, arXiv: 2111.09580 [math.GR] | DOI

[8] S. Turkelli, Splitting of Sharply 2-Transitive Groups of Characteristic 3, 5 Sep 2008, arXiv: 0809.0959 [math.GR] | MR

[9] M. Hall, Group Theor., IL, M., 1962 | MR

[10] E.B. Durakov, E.V. Bugaeva, I.V. Sheveleva, “On Sharply Doubly-Transitive Groups”, J. Sib. Fed. Univ. Math. Phys., 6 (2013), 28–32 | Zbl

[11] A.I. Sozutov, E.B. Durakov, “On exactly doubly transitive groups with generalized finite elements”, Sib. math. jur., 58:5 (2017), 1144–1149 | DOI | MR | Zbl

[12] A.I. Sozutov, “On Shunkov groups acting freely on Abelian groups”, Sib. math. journal, 54:1 (2013), 144–151 | DOI | MR | Zbl

[13] A.I. Sozutov, N.M. Suchkov, On some doubly transitive groups, Preprint No 17, INM SO RAN, Krasnoyarsk, 1998

[14] A.I. Sozutov, “Groups Saturated with Finite Frobenius Groups”, Mat. notes, 109:1 (2021), 270–279 | DOI | MR | Zbl

[15] A.I. Sozutov, N.M Suchkov, N.G. Suchkova, Infinite groups with involutions, Siberian Federal University, Krasnoyarsk, 2011

[16] V.D. Mazurov, “A characterization of alternating groups”, Algebra and logic, 44:1 (2005), 31–39 | DOI | MR | Zbl

[17] E.B. Durakov, “Sharply 3-transitive Groups with Finite Element”, Journal of Siberian Federal University. Mathematics $\$ Physics, 14:3 (2021), 344–350 | DOI | MR | Zbl

[18] D. Gorenstein, Finite simple groups, Mir, M., 1985 | MR | Zbl

[19] A.I. Sozutov, E.B. Durakov, “Local Finiteness of Periodic Sharply Triply Transitive Groups”, Algebra and Logic, 54:1 (2015), 48–57 | DOI | MR | Zbl

[20] K. Tent, “Sharply 3-tranzitive groups”, Advances in Mathematics, 286 (2014), 722–728 | DOI | MR

[21] A.I. Sozutov, O.V. Kravtsova, “On $KT$-Fields and Sharply Triply Transitive Groups”, Algebra and Logic, 57:2 (2018), 153–160 | DOI | MR | Zbl

[22] A.M. Popov, A.I. Sozutov, V.P. Shunkov, Groups with systems of Frobenius subgroups, KSTU Publishing House, Krasnoyarsk, 2004