Skip to main content
Log in

Sufficient conditions for the almost layer finiteness of groups

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We prove a theorem that describes almost layer-finite groups in the class of conjugatively biprimitive-finite groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. N. Chernikov,Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  2. V. I. Senashov, “Characterization of groups with the minimality condition for not almost layer-finite subgroups,”Ukr. Mat. Zh.,43, No. 7-8, 1002–1008 (1991).

    MATH  MathSciNet  Google Scholar 

  3. V. P. Shunkov, “The imbedding theorems for groups with involutions and the characterization of Chernikov groups,”Algebra Logika,27, No. 1, 100–121 (1988).

    MathSciNet  Google Scholar 

  4. V. P. Shunkov,On the Imbedding of Primary Elements in a Group [in Russian], Nauka, Novosibirsk (1992).

    Google Scholar 

  5. S. I. Adyan,The Burnside Problem and Identities in Groups [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  6. A. Yu. Ol'shanskii,Geometry of Defining Relations in a Group [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  7. N. G. Suchkova and V. P. Shunkov, “On groups with the minimality condition for Abelian subgroups,”Algebra Logika,25, No. 4, 445–469 (1986).

    MATH  MathSciNet  Google Scholar 

  8. V. P. Shunkov, “On periodic groups with almost regular involution,”Algebra Logika,11, No. 4, 470–493 (1972).

    Google Scholar 

  9. O. H. Kegel and B. A. F. Wehrfritz,Locally Finite Groups, North Holland, Amsterdam (1973).

    MATH  Google Scholar 

  10. B. Hartley, “Finite groups of automorphisms of locally soluble groups,”J. Algebra,57, No. 1, 242–257 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  11. I. I. Pavlyuk, A. A. Shafiro, and V. P. Shunkov, “On locally finite groups with the condition of primary minimality for subgroups,”Algebra Logika,13, No. 3, 324–336 (1974).

    MATH  Google Scholar 

  12. V. P. Shunkov, “On a class ofp-groups,”Algebra Logika,9, No. 4, 484–496 (1970).

    Google Scholar 

  13. R. Brauer and M. Suzuki, “On finite groups with an Abelian Sylow subgroup,”Can. J. Math.,14, 436–450 (1962).

    MATH  Google Scholar 

  14. M. I. Kargapolov, “Locally finite groups possessing normal systems with finite factors,”Sib. Mat. Zh.,2, No. 6, 853–873 (1961).

    MATH  MathSciNet  Google Scholar 

  15. N. S. Chernikov,On Infinitely Simple Locally Finite Groups [in Russian], Preprint No. 83.37, Institute of Mathematics, Academy of Sciences of USSR, Kiev (1982).

    Google Scholar 

  16. V. M. Busarkin and Yu. M. Gorchakov,Finite Splittable Groups [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  17. A. I. Sozutov and V. P. Shunkov, “On a generalization of the Frobenius theorem to infinite groups,”Mat. Sb.,100, No. 4, 495–508 (1976).

    MathSciNet  Google Scholar 

  18. V. P. Shunkov,M p -Groups [in Russian], Nauka, Moscow (1990).

    Google Scholar 

Download references

Authors

Additional information

Computer Center of the Siberian Division of the Russian Academy of Sciences, Krasnoyarsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 472–485, April, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Senashov, V.I. Sufficient conditions for the almost layer finiteness of groups. Ukr Math J 51, 525–537 (1999). https://doi.org/10.1007/BF02591757

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591757

Keywords

Navigation