Skip to main content
Log in

On Frobenius groups with noninvariant factor SL 2(3)

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain a nonsimplicity criterion of an infinite group containing an infinite class of Frobenius groups L g = 〈a, g −1 ag〉 with complement SL 2(3).

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, “On locally solvable groups that satisfy the condition of minimality for subgroups,” Mat. Sb., 28, No. 1, 119–129 (1951).

    MATH  Google Scholar 

  2. S. N. Chernikov, “On the theory of infinite special groups,” Mat. Sb., 7, No. 6, 539–548 (1968).

    Google Scholar 

  3. 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 

  4. M. I. Kargapolov, “On solvable groups of finite rank,” Algebra Logika, 1, No. 5, 37–44 (1962).

    MATH  MathSciNet  Google Scholar 

  5. V. P. Shunkov, “On one generalization of the Frobenius theorem to periodic groups,” Algebra Logika, 6, No. 3, 113–124 (1967).

    MATH  Google Scholar 

  6. V. P. Shunkov, “On one class of p-groups,” Algebra Logika, 9, No. 4, 484–496 (1970).

    MATH  Google Scholar 

  7. G. Frobenius, Uber Auflosbare Gruppen. IV, Sitzungsber. Press. Akad. Wiss. Berlin (1901), pp. 1216–1230.

  8. V. M. Busarkin and A. I. Starostin, “On locally finite decomposable groups,” Usp. Mat. Nauk, 17, No. 6, 275–294 (1962).

    Google Scholar 

  9. V. M. Busarkin and A. I. Starostin, “On decomposable locally finite groups,” Mat. Sb., 62, No. 3, 275–294 (1963).

    MATH  MathSciNet  Google Scholar 

  10. V. P. Shunkov, “On one criterion for the nonsimplicity of groups,” Algebra Logika, 14, No. 5, 576–603 (1975).

    MATH  Google Scholar 

  11. L. Kh. Zhurtov and V. D. Mazurov, “On Frobenius groups generated by quadratic elements,” in: Abstracts of the International Seminar on Group Theory [in Russian], Ekaterinburg (2001), pp. 77–81.

  12. A. I. Starostin, “On Frobenius groups,” Ukr. Mat. Zh., 23, No. 5, 629–639 (1971).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  14. A. Kh. Zhurtov, Quadratic Elements of Frobenius Groups [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Nal’chik (2003).

  15. A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 765–777, June, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozulin, S.N., Senashov, V.I. & Shunkov, V.P. On Frobenius groups with noninvariant factor SL 2(3). Ukr Math J 58, 862–875 (2006). https://doi.org/10.1007/s11253-006-0109-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0109-2

Keywords

Navigation