References
J. G. Thompson, “Finite groups with fixed-point-free automorphisms of prime order,” Proc. Nat. Acad. Sci. U.S.A.,45, 578–581 (1959)
G. Higman, “Groups and rings which have automorphisms without non-trivial fixed elements,” J. London Math. Soc. (2),32, 321–334 (1957).
V. A. Kreknin and A. I. Kostrikin, “Lie algebras with regular automorphisms,” Dokl. Akad. Nauk SSSR,149, No. 2, 249–251 (1963).
V. A. Kreknin, “Solvability of Lie algebras with regular automorphisms of finite period,” Dokl. Akad. Nauk SSSR,150, No. 3, 467–469 (1963).
P. Fong, “On orders of finite groups and centralizers ofp-elements,” Osaka J. Math.,13, 483–489 (1973).
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).
J. Alperin, “Automorphisms of solvable groups,” Proc. Amer. Math. Soc.,13, 175–180 (1962).
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).
E. I. Khukhro, “Lie rings and groups admitting an almost regular automorphism of prime order,” Mat. Sb.,181, No. 9, 1207–1219 (1990).
Yu. Medvedev,p-Groups, Liep-Rings andp-Automorphisms;p-Divided Lie Rings andp-Groups [Preprints], Wisconsin Univ., Madison (1994).
L. G. Kovács, “Groups with regular automorphisms of order four,” Math. Z., No. 75, 277–294 (1961).
A. Shalev, “Automorphisms of finite groups of bounded rank,” Israel J. Math.,82, 395–404 (1993).
A. Lubotzky and A. Mann, “Powerfulp-groups. I: finite groups,” J. Algebra,105, 484–505 (1987).
A. Shalev, “On almost fixed point free automorphisms,” J. Algebra,157, 271–282 (1993).
E. I. Khukhro, “Finitep-groups admittingp-automorphisms with few fixed points,” Mat. Sb.,184, No. 12, 53–64 (1993).
J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal, Analytic Pro-p-Groups, Cambridge Univ., Cambridge (1991).
M. F. Newman, “The soluble length of soluble linear groups,” Math. Z.,126, 59–70 (1972).
Author information
Authors and Affiliations
Additional information
This research was supported by the Russian Foundation for Basic Research (Grant 94-01-00048) and the International Science Foundation and the Government of the Russian Federation (Grant NQ7300).
Translated from Sibirskii Matematicheskii, Vol. 37, No. 6, pp. 1407–1412, November–December, 1996.
Rights and permissions
About this article
Cite this article
Khukhro, E.I. Almost regular automorphisms of finite groups of bounded rank. Sib Math J 37, 1237–1241 (1996). https://doi.org/10.1007/BF02106748
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02106748