Geodesic
2-rank two periodic groups saturated with finite simple groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 786-796.

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It is proved that a periodic group of 2-rank two, saturated with finite simple groups, is locally finite and is isomorphic to one of the groups $ L_2 (Q), A_7, L_3 (P), U_3 (R), M_ {11}, U_3 (4) $, where $Q,P,R$ are suitable locally finite fields of odd characteristics and $|Q|> 3$.
Keywords: periodic group, simple groups.
Mots-clés : saturation 
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D. V. Lytkina; A. I. Sozutov; A. A. Shlepkin. 2-rank two periodic groups saturated with finite simple groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 786-796. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a21/

[1] V.V. Belyaev, “Lokal'no konechnye gruppy Shevalle”, Issledovaniya po teorii grupp, 150, UNC AN SSSR, Sverdlovsk, 1984, 39–50

[2] A.V. Borovik, “Imbeddings of finite Chevalley groups and periodic linear groups”, Sib. mat. journal, 24:6 (1983), 26–35 | MR | Zbl

[3] D. Gorenstejn, Konechnye prostye gruppy, Mir, M., 1985

[4] A. Kh. Zhurtov, “On regular automorphisms of order 3 and Frobenius pairs”, Siberian Mathematical Journal, 41:2 (2000), 329–338 | DOI | MR | Zbl

[5] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, Nauka, M., 1982 | MR | Zbl

[6] A.A. Kuznetsov, K.A. Filippov, “Groups saturated by a given set of groups”, Siberian Eltctronic Mathematical Reports, 8 (2011), 230–246 | MR | Zbl

[7] D.V. Lytkina, L.R. Tukhvatullin, K.A. Filippov, “On periodic groups, saturated by a finite set of finite simple groups”, Siberian Mathematical Journal, 49:2 (2008), 394–399 | DOI | MR | Zbl

[8] D.V. Lytkina, A.A. Shlepkin, “Periodic groups saturated with finite simple groups of types $U_3$ and $L_3$”, Algebra and Logic, 55:4 (2016), 441–448 | DOI | MR | Zbl

[9] D.V. Lytkina, A.A. Shlepkin, “Periodic groups saturated by linear groups of degree 2 and unitary groups of degree 3 over finite fields of odd characteristics”, Mat. trudy, 21:1 (2018), 55–72 | MR

[10] A.I. Mal'cev, “Ob izomorfnom predstavlenii beskonechnyh grupp matricami”, Mat. sb., 8:3 (1940), 405–422 | MR | Zbl

[11] B. Dzh. Li, D.V. Lytkina, “O silovskih 2-podgruppah periodicheskih grupp, nasyshchennyh konechnymi prostymi gruppami”, Sibirskij matematicheskij zhurnal, 57:6 (2016), 1313–1319 | MR

[12] A.G. Rubashkin, K.A. Filippov, “O periodicheskih gruppah, nasyshchennyh gruppami $L_2(p^n)$”, Sibirskij matematicheskij zhurnal, 46:6 (2005), 1388–1392 | MR | Zbl

[13] M. Holl, Teoriya grupp, IL, M., 1962

[14] A.K. Shlepkin, A.G. Rubashkin, “Ob odnom klasse periodicheskikh grupp”, Algebra i logika, 44:1 (2005), 114–125 | MR | Zbl

[15] A.K. Shlepkin, “Sopryazhenno biprimitivno konechnye gruppy, soderzhashchie konechnye nerazreshimye podgruppy”, Tret'ya mezhdunar. konf. po algebre, Sb. tez. (Krasnoyarsk, 1993)

[16] V.P. Shunkov, “On one class of $p$ — groups”, Algebra end logika, 9:4 (1970), 484–496 | MR

[17] V.P. Shunkov, “O periodicheskih gruppah s pochti regulyarnoj involyuciej”, Algebra end logika, 11 (1972), 470–494 | MR

[18] Alperin J. L., Brauer R., Gorenstein D., “Finite groups wish quasi-dihedral and wreathed Sylow 2-subgroup”, Trans. AMS, 151 (1970), 1–261 | MR | Zbl

[19] J.L. Alperin, R. Brauer, D. Gorenstein, “Finite simple groups of 2-rang two”, Collection of articles dedicated to the memori of Abraham Adrian Albert, Scripta Math., 29, no. 3–4, 1973, 191–214 | MR | Zbl

[20] Carter R. W., Simple groups of Lie type, Wiley and Sons, New York, 1972 | MR | Zbl

[21] Hartley B., Shute G., “Monomorphisms and direct limits of finite groups of Lie type”, The Quarterly Journal of Mathematics Oxford (2), 35:137 (1984), 49–71 | DOI | MR | Zbl

[22] John N. Bray, Derek F. Holt, Colva M. Ronty-Dougal, The Maximal Subgroups of the Low — Dimensional Finite Classical groups, Cambridge university press, Cambridge, 2013 | MR | Zbl

[23] Kegel O. N., Wehrfritz B. A. F., Locally Finite Groups, North-Holland, Amsterdam, 1973 | MR | Zbl

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

[25] Thomas S., “The classification of the simple periodic linear groups”, Arch. Math., 41:2 (1983), 103–116 | DOI | MR | Zbl