Characterizations of simple linear groups in the class of periodic groups
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 287-292.

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This paper is a survey of some results about the structure of periodic groups saturated with finite simple groups of Lie type. It is based on a talk of authors given on the XI workshop on Group theory dedicated to the 70-th anniversary of A. Yu. Olshanskiy (Krasnoyarsk, July 27–August 2, 2016).
Keywords: linear group, periodic group, locally finite group.
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Daria V. Lytkina; Victor D. Mazurov. Characterizations of simple linear groups in the class of periodic groups. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 287-292. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a2/

[1] C. W. Curtis, I. Reiner, Representation Theory of Finite groups and Associative Algebras, John Wiley Sons, New York–London, 1962 | MR | Zbl

[2] O. Kegel, “Über einfache, local endliche Gruppen”, Math. Z., 95 (1967), 169–195 | DOI | MR | Zbl

[3] D. J. Winter, “Representations of locally finite groups”, Bull. Amer. Math. Soc., 74 (1968), 145–148 | DOI | MR | Zbl

[4] M. J. Larsen, R. Pink, “Finite subgroups of algebraic groups”, J. Amer. Math. Soc., 24:4 (2011), 1105–1158 | DOI | MR | Zbl

[5] V.V. Belyaev, “Locally finite Chevalley groups”, Studies in Group Theory, Ural'sky Nauchny Tsentr AS USSR, Sverdlovsk, 1984, 39–50 (in Russian) | MR

[6] A. V. Borovik, “Embeddings of finite Chevalley groups and periodic linear groups”, Siberian Math. J., 24:6 (1983), 843–851 | DOI | MR | Zbl

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

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

[9] Unsolved Problems in Group Theory, The Kourovka Notebook, 18, Institut matematiki, Novosibirsk, 2014 (in Russian)

[10] R. W. Carter, Simple groups of Lie type, John Wiley Sons, London, 1972 | MR | Zbl

[11] A. I. Malcev, “On isomorphic matrix representations of infinite groups”, Rec. Math (Mat. Sbornik), N.S., 8(50):3 (1940), 405–422 (in Russian) | MR | Zbl

[12] A. Yu. Olshanskii, “Embedding of countable periodic groups in simple 2-generator periodic groups”, Ukrain. Mat. Zh., 43:7–8 (1991), 980–986 | MR

[13] A. G. Rubashkin, K. A. Filippov, “Periodic groups saturated with the groups $L_2(p^n)$”, Siberian Math. J., 46:6 (2005), 1119–1122 | DOI | MR | Zbl

[14] D. V. Lytkina, A. A. Shlöpkin, “Periodic groups saturated with finite simple groups of the types $U_3$ and $L_3$”, Algebra and Logic, 2016 (to appear) | MR

[15] K. A. Filippov, Groups saturated with finite nonabelian groups and their extension, PhD thesis, Krasnoyarsk, 2005

[16] K.A. Filippov, “On periodic groups saturated by finite simple groups”, Siberian Math. J., 53:2 (2012), 345–351 | DOI | MR | Zbl

[17] A. K. Shlöpkin, “On some periodic groups saturated by finite simple groups”, Mat. Tr., 1:1 (1998), 129–138 (in Russian) | MR | Zbl

[18] B. D. Li, D. V. Lytkina, “On Sylow 2-subgroups of periodic groups saturated with finite simple groups”, Sib. Math. J., 2016 (to appear) | MR