Geodesic
Semisimple groups that have a faithful finitary permutation representation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 55-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that a locally finite semisimple group has a faithful finitary permutation representation if and only if any of its residually finite subgroups is locally normal.
Keywords: finitary permutation groups. 
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V. V. Belyaev; D. A. Shved. Semisimple groups that have a faithful finitary permutation representation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 55-62. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a4/

[1] Aschbacher M., Finite group theory, Cambridge University Press, Cambridge, 1993, 274 pp. | MR | Zbl

[2] Dixon J. D., Mortimer B., Permutation groups, Springer-Verlag, N.Y., 1996, 346 pp. | MR | Zbl

[3] Hall P., “Periodic FC-groups”, J. London Math. Soc., 34 (1959), 289–304 | DOI | MR | Zbl

[4] Kegel O. H., Wehrfritz B. A. F., Locally finite groups, North-Holland Publishing Company, Amsterdam, 1973, 210 pp. | MR | Zbl

[5] Leinen F., Puglisi O., “Finitary representations and images of transitive finitary permutation groups”, J. Algebra, 222:2 (1999), 524–549 | DOI | MR | Zbl

[6] Neumann P., “The structure of finitary permutation groups”, Arch. Math., 27:3 (1976), 3–17 | DOI | MR | Zbl

[7] Wiegold J., “Groups of finitary permutations”, Arch. Math., 25 (1974), 466–469 | DOI | MR | Zbl

[8] Ado I. D., “O podgruppakh schetnoi simmetricheskoi”, Dokl. AN SSSR, 50 (1945), 15–17 | MR | Zbl

[9] Belyaev V. V., “Lokalnye kharakterizatsii beskonechnykh znakoperemennykh grupp i grupp lievskogo tipa”, Algebra i logika, 31:4 (1992), 369–390 | MR | Zbl

[10] Belyaev V. V., “Stroenie $p$-grupp konechnykh preobrazovanii”, Algebra i logika, 31:5 (1992), 453–478 | MR | Zbl

[11] Belyaev V. V., “Neprivodimye periodicheskie gruppy finitarnykh preobrazovanii”, Algebra i logika, 33:2 (1994), 109–134 | MR | Zbl

[12] Belyaev V. V., “Gruppy s finitarnymi klassami sopryazhennykh elementov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19, no. 3, 2013, 45–61

[13] Suprunenko D. A., “O lokalno nilpotentnykh podgruppakh beskonechnoi simmetricheskoi gruppy”, Dokl. AN SSSR, 167:2 (1966), 302–304 | MR

[14] Suprunenko D. A., “O nerazlozhimosti tranzitivnykh podgrupp gruppy $\operatorname{SF}(X)$”, Dokl. AN SSSR, 186:4 (1969), 779–780 | MR | Zbl

[15] Suprunenko D. A., Gruppy matrits, Nauka, Moskva, 1972, 350 pp. | MR | Zbl

[16] Shved D. A., “Finitarnye avtomorfizmy poluprostykh grupp”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 312–315