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Siberian Mathematical Journal

, Volume 37, Issue 6, pp 1237–1241 | Cite as

Almost regular automorphisms of finite groups of bounded rank

  • E. I. Khukhro
Article

Keywords

Finite Group Regular Automorphism Bounded Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. G. Thompson, “Finite groups with fixed-point-free automorphisms of prime order,” Proc. Nat. Acad. Sci. U.S.A.,45, 578–581 (1959)Google Scholar
  2. 2.
    G. Higman, “Groups and rings which have automorphisms without non-trivial fixed elements,” J. London Math. Soc. (2),32, 321–334 (1957).Google Scholar
  3. 3.
    V. A. Kreknin and A. I. Kostrikin, “Lie algebras with regular automorphisms,” Dokl. Akad. Nauk SSSR,149, No. 2, 249–251 (1963).Google Scholar
  4. 4.
    V. A. Kreknin, “Solvability of Lie algebras with regular automorphisms of finite period,” Dokl. Akad. Nauk SSSR,150, No. 3, 467–469 (1963).Google Scholar
  5. 5.
    P. Fong, “On orders of finite groups and centralizers ofp-elements,” Osaka J. Math.,13, 483–489 (1973).Google Scholar
  6. 6.
    B. Hartley and T. Meixner, “Finite soluble groups containing an element of prime order whose centralizer is small,” Arch. Math. (Basel),36, 211–213 (1981).Google Scholar
  7. 7.
    J. Alperin, “Automorphisms of solvable groups,” Proc. Amer. Math. Soc.,13, 175–180 (1962).Google Scholar
  8. 8.
    E. I. Khukhro, “Finitep-groups admitting an automorphism of orderp with a small number of fixed points,” Mat. Zametki,38, No. 5, 652–657 (1985).Google Scholar
  9. 9.
    E. I. Khukhro, “Lie rings and groups admitting an almost regular automorphism of prime order,” Mat. Sb.,181, No. 9, 1207–1219 (1990).Google Scholar
  10. 10.
    Yu. Medvedev,p-Groups, Liep-Rings andp-Automorphisms;p-Divided Lie Rings andp-Groups [Preprints], Wisconsin Univ., Madison (1994).Google Scholar
  11. 11.
    L. G. Kovács, “Groups with regular automorphisms of order four,” Math. Z., No. 75, 277–294 (1961).CrossRefGoogle Scholar
  12. 12.
    A. Shalev, “Automorphisms of finite groups of bounded rank,” Israel J. Math.,82, 395–404 (1993).Google Scholar
  13. 13.
    A. Lubotzky and A. Mann, “Powerfulp-groups. I: finite groups,” J. Algebra,105, 484–505 (1987).CrossRefGoogle Scholar
  14. 14.
    A. Shalev, “On almost fixed point free automorphisms,” J. Algebra,157, 271–282 (1993).CrossRefGoogle Scholar
  15. 15.
    E. I. Khukhro, “Finitep-groups admittingp-automorphisms with few fixed points,” Mat. Sb.,184, No. 12, 53–64 (1993).Google Scholar
  16. 16.
    J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal, Analytic Pro-p-Groups, Cambridge Univ., Cambridge (1991).Google Scholar
  17. 17.
    M. F. Newman, “The soluble length of soluble linear groups,” Math. Z.,126, 59–70 (1972).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. I. Khukhro
    • 1
  1. 1.Novosibirsk

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