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Siberian Mathematical Journal

, Volume 47, Issue 4, pp 740–750 | Cite as

On the existence of f-local subgroups in a group

  • A. I. Sozutov
  • M. V. Yanchenko
Article

Abstract

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.

Keywords

group f-local subgroup almost finite element generally finite element generally finite group 

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References

  1. 1.
    Strunkov N. P., “Subgroups of periodic groups,” Dokl. Akad. Nauk SSSR, 170, No. 2, 279–281 (1966).zbMATHMathSciNetGoogle Scholar
  2. 2.
    Strunkov N. P., “Normalizers and abelian subgroups of some classes of groups,” Izv. Akad. Nauk SSSR Ser. Mat., 31, No. 3, 657–670 (1967).zbMATHMathSciNetGoogle Scholar
  3. 3.
    Shunkov V. P., “Abelian subgroups in biprimitive finite groups,” Algebra i Logika, 12, No. 5, 603–614 (1973).zbMATHMathSciNetGoogle Scholar
  4. 4.
    Shunkov V. P., “On infinite centralizers in groups,” Algebra i Logika, 13, No. 2, 224–226 (1974).zbMATHMathSciNetGoogle Scholar
  5. 5.
    Shunkov V. P., “On sufficient criteria of the existence of infinite locally finite subgroups in a group,” Algebra i Logika, 15, No. 6, 716–737 (1976).zbMATHMathSciNetGoogle Scholar
  6. 6.
    Sozutov A. I. and Shunkov V. P., “On infinite groups saturated with Frobenius subgroups,” Algebra i Logika, 16, No. 6, 711–735 (1977).zbMATHMathSciNetGoogle Scholar
  7. 7.
    Sozutov A. I., On the Existence of Infinite Subgroups with Nontrivial Locally Finite Radical in a Group [in Russian] [Preprint], Krasnoyarsk. Vychisl. Tsentr Sibirsk. Otdel. Akad. Nauk SSSR, Krasnoyarsk (1980).Google Scholar
  8. 8.
    Shunkov V. P., “Embedding theorems for groups with involution and characterization of Chernikov groups,” Algebra i Logika, 27, No. 1, 100–121 (1988).zbMATHMathSciNetGoogle Scholar
  9. 9.
    Shunkov V. P., Embedding Primary Elements in a Group [in Russian], Nauka, Novosibirsk (1992).Google Scholar
  10. 10.
    Sozutov A. I., “On the existence of f-local subgroups in a group,” Algebra i Logika, 36, No. 5, 573–598 (1997).zbMATHMathSciNetGoogle Scholar
  11. 11.
    Sozutov A. I. and Yanchenko M. V., “On one criterion of existence of f-local subgroups in a group,” in: Abstracts: V International Conference “Algebra and Number Theory: Contemporary Problems and Applications” [in Russian], Tula, May 19–20, 2003, Tula, Izdat. TGPU, 2003, pp. 208–210.Google Scholar
  12. 12.
    Sozutov A. I. and Yanchenko M. V., “On criteria of the existence of f-local subgroups in a group,” in: Abstracts: International Conference on Mathematics and Mechanics [in Russian], Tomsk, September 16–18, 2003, Tomsk, Izdat. TGU, 2003, pp. 55–56.Google Scholar
  13. 13.
    The Kourovka Notebook. Unsolved Problems in Group Theory. Vol. 15, Inst. Math. (Novosibirsk), Novosibirsk (2002).Google Scholar
  14. 14.
    Adyan S. I., The Burnside Problem and Identities in Groups [in Russian], Nauka, Moscow (1975).Google Scholar
  15. 15.
    Senashov V. I., Shunkov V. P., and Yakovleva E. N., “Groups with finite periodic part,” in: Abstracts: International Conference “Algebra and Its Applications”, Krasnoyarsk, 2002, pp. 105–106.Google Scholar
  16. 16.
    Shunkov V. P., T 0-Groups [in Russian], Nauka, Sibirsk. Izdat. Firma Ross. Akad. Nauk, Novosibirsk (2000).Google Scholar
  17. 17.
    Gorenstein D., Finite Simple Groups. An Introduction to Their Classification [Russian translation], Mir, Moscow (1985).Google Scholar
  18. 18.
    Busarkin V. M. and Gorchakov Yu. M., Decomposable Finite Groups [in Russian], Nauka, Moscow (1968).Google Scholar
  19. 19.
    Sozutov A. I. and Shlepkin A. K., “On groups with a normal splitting component,” Siberian Math. J., 38, No. 4, 777–790 (1997).zbMATHMathSciNetGoogle Scholar
  20. 20.
    Cherep A. A., “On infinite Frobenius groups,” submitted to VINITI on March 11, 1991, No. 1014-B-91.Google Scholar
  21. 21.
    Gorchakov Yu. M., Groups with Finite Classes of Conjugate Elements [in Russian], Nauka, Moscow (1978).Google Scholar
  22. 22.
    Shunkov V. P., “Periodic groups with almost regular involution,” Algebra i Logika, 11, No. 4, 478–494 (1972).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. I. Sozutov
    • 1
  • M. V. Yanchenko
    • 1
  1. 1.Krasnoyarsk State University of Architecture and BuildingKrasnoyarskRussia

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