Abstract
The structure of periodic irreducible primitive groups of finitary transformations of an infinitedimensional space is investigated. Every such group is shown to be a holomorph of some simple group whose action on a space is irreducible and primitive also.
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References
V. V. Belyaev, “The structure ofp-groups of finitary transformations,”Algebra Logika,31, No. 5, 453–478 (1992).
V. V. Belyaev, “Locally solvable periodic groups of finitary transformations,”Algebra Logika,31, No. 6, 569–591 (1992).
V. V. Belyaev, “Semisimple periodic groups of finitary transformations,”Algebra Logika,32, No. 1, 17–33 (1993).
V. V. Belyaev, “Local characterizations of periodic simple groups of finitary transformations,”Algebra Logika,32, No. 3, 231–250 (1993).
V. V. Belyaev, “Locally finite Chevalley groups,” in:Studies on Group Theory [in Russian], Sverdlovsk (1984), pp. 39-50.
Yu. I. Merzlyakov,Rational Groups [in Russian], Nauka, Moscow (1980).
R. Steinberg,Lectures on Chevalley Groups, Yale University Notes (1967).
M. I. Kargapolov and Yu. I. Merzlyakov,Foundations of Group Theory [in Russian], Nauka, Moscow (1982).
L. A. Skornyakov,Elements of Structure Theory [in Russian], Nauka, Moscow (1970).
H. Wielandt,Unendliche Permutationsgruppen, Vorlesungen, Tübingen (1959–1960).
J. I. Hall, “Infinite alternating groups as finitary linear transformation groups,”J. Algebra,119, No. 2, 337–359 (1988).
R. E. Phillips, “The structure of Groups of Finitary Transformations,”J. Algebra,119, No. 2, 400–448 (1988).
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Translated fromAlgebra i Logika, Vol. 33, No. 2, pp. 109-134, March-April, 1994.
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Belyaev, V.V. Irreducible periodic groups of finitary transformations. Algebr Logic 33, 65–78 (1994). https://doi.org/10.1007/BF00739992
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DOI: https://doi.org/10.1007/BF00739992