Advertisement

Algebra and Logic

, Volume 58, Issue 1, pp 15–22 | Cite as

Some Periodic Groups Admitting a Finite Regular Automorphism of Even Order

  • E. B. DurakovEmail author
  • A. I. Sozutov
Article
  • 3 Downloads

We study the structure of an infinite group with automorphism of order 2p, where p is an odd prime leaving only the identity element fixed.

Keywords

periodic group Frobenius group locally finite group automorphism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Fischer, “Finite groups admitting a fixed-point-free automorphism of order 2p,” J. Alg., 3, No. 1, 99-114 (1966).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    B. Fischer, “Finite groups admitting a fixed-point-free automorphism of order 2p. II,” 5, No. 1, 25-40 (1967).Google Scholar
  3. 3.
    D. Gorenstein, Finite Simple Groups, An Introduction to Their Classification, Plenum, New York (1982).zbMATHGoogle Scholar
  4. 4.
    S. I. Adyan, The Burnside Problem and Identities in Groups [in Russian], Nauka, Moscow (1975).zbMATHGoogle Scholar
  5. 5.
    A. I. Sozutov amd E. B. Durakov, “On sharply 2-transitive groups with generalized finite elements,” Sib. Math. J., 58, No. 5, 887-890 (2017).Google Scholar
  6. 6.
    A. I. Sozutov, “Groups admitting a finite regular automorphism of even order,” Proc. Int. Conf. “Modern Problems in Applied Mathematics and Physics,” Nalchik (2017), pp. 193/194.Google Scholar
  7. 7.
    A. I. Sozutov amd E. B. Durakov, Proc. All-Russian Conf. “Algebra, Analysis, and Related Problems of Mathematical Modeling,” Vladikavkaz (2017), p. 45.Google Scholar
  8. 8.
    A. M. Popov, A. I. Sozutov, and V. P. Shunkov, Groups with Systems of Frobenius Subgroups [in Russian], Krasnoyarsk State Techn. Univ., Krasnoyarsk (2004).Google Scholar
  9. 9.
    H. Neumann, Varieties of Groups, Springer, Berlin (1967).CrossRefzbMATHGoogle Scholar
  10. 10.
    M. Hall, The Theory of Groups, Macmillan, New York (1959).zbMATHGoogle Scholar
  11. 11.
    V. P. Shunkov, “Characterization of some finite Frobenius groups,” Mat. Zametki, 434, No. 6, 725-732 (1988).MathSciNetzbMATHGoogle Scholar
  12. 12.
    V. P. Shunkov, “On Frobenius pairs of the form (FλV,V ),” Mat. Sb., 180, No. 10, 1311-1324 (1989).MathSciNetGoogle Scholar
  13. 13.
    V. M. Busarkin and Yu. M. Gorchakov, Finite Groups That Admit Partitions [in Russian], Nauka, Moscow (1968).Google Scholar
  14. 14.
    A. I. Sozutov and A. K. Shlepkin, “On groups with a normal splitting component,” Sib. Math. J., 38, No. 4, 777-790 (1997).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    E. I. Khukhro, Nilpotent Groups and Their Automorphisms of Prime Order, Freiburg (1992).Google Scholar
  16. 16.
    V. A. Kreknin and A. I. Kostrikin, “Lie algebras with regular automorphisms,” Dokl. Akad. Nauk SSSR, 149, No. 2, 249-251 (1963).MathSciNetzbMATHGoogle Scholar
  17. 17.
    D. Gorenstein and I. N. Herstein, “Finite groups admitting a fixed-point-free automorphism of order 4, Am. J. Math., 83, 71-78 (1961).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

Personalised recommendations