Skip to main content
Log in

KT-Fields and Sharply Triply Transitive Groups

  • Published:
Algebra and Logic Aims and scope

We study KT-fields and sharply triply transitive groups with a finite or perfect involution stabilizing at least one point.

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. M. Hall, The Theory of Groups [Russian translation], IL, Moscow (1962).

    Google Scholar 

  2. H. Wähling, Theorie der Fastkörper, Thalen Ferlag, Essen (1987).

    MATH  Google Scholar 

  3. H. Zassenhaus, “Über endliche Fastkörper,” Abh. Math. Semin. Univ. Hamb., 11, 187-220 (1936).

    Article  MATH  Google Scholar 

  4. O. H. Kegel, “Zur Struktur lokal endlicher Zassenhausgruppen,” Arch. Math., 18, 337-348 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  5. V. D. Mazurov, “Sharply doubly transitive groups,” Trudy Inst. Mat. SO RAN, 30, 114-118 (1996).

    MATH  Google Scholar 

  6. T. Grundhöfer and E. Jabara, “Fixed-point-free 2-finite automorphism groups,” Arch. Math., 97, No. 3, 219-223 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. I. Sozutov, “On the Shunkov groups acting freely on Abelian groups,” Sib. Math. J., 54, No. 1, 144-151 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  8. E. B. Durakov, E. V. Bugaeva, and I. V. Sheveleva, “On sharply doubly-transitive groups,” Zh. SFU, Ser. Mat. Fiz., 6, No. 1, 28-32 (2013).

    Google Scholar 

  9. A. I. Sozutov, E. B. Durakov, and E. V. Bugaeva, “On certain near-domains and sharply 2-transitive groups,” Trudy Inst. Mat. Mekh. UrO RAN, 20, No. 2, 277-283 (2014).

    Google Scholar 

  10. A. I. Sozutov and E. B. Durakov, “Local finiteness of periodic sharply triply transitive groups,” Algebra and Logic, 54, No. 1, 48-57 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Rips, Y. Segev, and K. Tent, “A sharply 2-transitive group without a non-trivial abelian normal subgroup,” arXiv:1406.0382; https://arxiv.org/abs/1406.0382v5.

  12. K. Tent and M. Ziegler, “Sharply 2-transitive groups,” Adv. Geom., 16, No. 1, 131-134 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  13. K. Tent, “Sharply 3-transitive groups,” Adv. Math., 286, 722-728 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Kerby and H. Wefelscheid, “¨Uber eine scharf 3-fach transitiven Gruppen zugeordnete algebraische Struktur,” Abh. Math. Semin. Univ. Hamb., 37, 225-235 (1972).

    Article  MATH  Google Scholar 

  15. V. V. Belyaev, “Groups with an almost regular involution,” Algebra and Logic, 26, No. 5, 315-317 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  16. V. D. Mazurov, “Infinite groups with Abelian centralizers of involutions,” Algebra and Logic, 39, No. 1, 42-49 (2000).

  17. A. I. Sozutov, “Some infinite groups with strongly embedded subgroup,” Algebra and Logic, 39, No. 5, 345-353 (2000).

    Article  MathSciNet  Google Scholar 

  18. A. I. Sozutov and N. M. Suchkov, “On infinite groups with a given strongly isolated 2-subgroup,” Mat. Zametki, 68, No. 2, 273-285 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  19. N. M. Suchkov, “Finiteness of some sharply doubly transitive groups,” Algebra and Logic, 40, No. 3, 190-193 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  20. A. I. Sozutov, “Frobenius pairs with perfect involutions,” Algebra and Logic, 44, No. 6, 422-428 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  21. A. I. Sozutov and A. S. Kryukovskii, “Groups with elementary Abelian centralizers of involutions,” Algebra and Logic, 46, No. 1, 46-49 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  22. A. I. Sozutov, “Groups with an almost regular involution,” Algebra and Logic, 46, No. 3, 195-199 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  23. A. I. Sozutov, N. M. Suchkov, and N. G. Suchkova, Infinite Groups with Involutions [in Russian], Siberian Federal University, Krasnoyarsk (2011).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Sozutov.

Additional information

Translated from Algebra i Logika, Vol. 57, No. 2, pp. 232-242, March-April, 2018.

A. I. Sozutov and O. V. Kravtsova Supported by RFBR, project 15-01-04897-a.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sozutov, A.I., Kravtsova, O.V. KT-Fields and Sharply Triply Transitive Groups. Algebra Logic 57, 153–160 (2018). https://doi.org/10.1007/s10469-018-9487-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-018-9487-4

Keywords

Navigation