Abstract
It is proved that some groups with a strongly isolated 2-subgroup of period not exceeding four are locally finite. In particular, the positive answer to Shunkov’s question 10.76 in the Kourovka notebook is obtained.
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References
Unsolved Problems in Group Theory. The Kourovka Notebook [in Russian], 6th–14th editions, Novosibirsk (1978–1999).
A. I. Sozutov, “On groups with a strongly embedded subgroup,” in:International Conference “Symmetry in Science” [in Russian], Abstracts of Papers, Krasnoyarsk (1998), pp. 121–123.
A. I. Sozutov and N. M. Suchkov, “On some infinite multiply transitive groups,” in:International Algebraic Seminar Dedicated to the 70th Anniversary of the Chair of Higher Algebra of the Moscow State University (February 10–12, 1999) [in Russian], Abstracts of Papers, Moscow (1999), p. 52.
A. I. Sozutov, “On some infinite groups with a strongly embedded subgroup,”Algebra i Logika [Algebra and Logic] (to appear).
M. Suzuki, “On a class of doubly transitive groups,”Ann. of Math.,75, No. 1, 105–145 (1961).
G. Higman, “Suzuki 2-groups,”Illinois J. Math.,7, 79–96 (1963).
D. Gorenstein,Finite Simple Groups. An Introduction to Their Classification, Plenum Publishing Co., New York (1982).
A. I. Sozutov, “On groups with the class of Frobenius-abelian elements,”Algebra i Logika [Algebra and Logic],34, No. 5, 531–549 (1995).
V. M. Busarkin and Yu. M. Gorchakov,Finite Splittable Groups [in Russian], Nauka, Moscow (1968).
A. I. Sozutov and N. M. Suchkov,On Some Doubly Transitive Groups [in Russian], Preprint No. 242 17, Institute of Computer Mathematics of the Siberian Division of the Russian Academy of Sciences, Krasnoyarsk (1998), p. 24.
A. I. Sozutov and N. M. Suchkov,On Infinite Z-Groups with Given Stabilizers of Points [in Russian], Dep. VINITI 09.03.99 No. 242 700-B99, Krasnoyarsk State Academy of Architecture and Building, Krasnoyarsk (1999).
A. I. Sozutov and V. P. Shunkov, “A generalization of the Frobenius theorem to infinite groups,”Mat. Sb. [Math. USSR-Sb.],100, No. 4, 495–506 (1976).
V. V. Belyaev, “Groups with almost regular involution,”Algebra i Logika [Algebra and Logic],26, No. 5, 531–535 (1987).
A. I. Starostin, “On Frobenius groups,”Ukrain. Mat. Zh. [Ukrainian Math. J.],23, No. 5, 629–639 (1971).
M. I. Kargapolov and Yu. I. Merzlyakov,Foundations of the Theory of Groups [in Russian], Nauka, Moscow (1977).
H. Zassenhaus, “Kennzeichnung endlicher linearen Gruppen als Permutationsgruppen,”Abh. Math. Sem. Hamburg.,11, 17–40 (1936).
M. Hall,The Theory of Groups, Macmillan, New York (1959).
N. M. Suchkov, “Automorphically factorizable groups,”Algebra i Logika [Algebra and Logic],18, No. 4, 481–487 (1979).
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Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 272–285, August, 2000.
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Sozutov, A.I., Suchkov, N.M. On infinite groups with a given strongly isolated 2-subgroup. Math Notes 68, 237–247 (2000). https://doi.org/10.1007/BF02675349
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DOI: https://doi.org/10.1007/BF02675349