This is a preview of subscription content, log in via an institution to check access.
References
Fong P., “On orders of finite groups and centralizers ofp-elements,” Osaka J. Math.,13, 483–489 (1976).
Hartley B. andMeixner T., “Finite soluble groups containing an element of prime order whose centralizer is small,” Arch. Math.,36, 211–213 (1981).
Khukhro E. I., “Finitep-groups admitting an automorphism of orderp with a small number of fixed points,” Mat. Zametki,38, No. 5, 652–657 (1985). English transl.: Math. Notes,38, 867–870 (1986).
Khukhro E. I., “Groups and Lie rings admitting an almost regular automorphism of prime order,” Mat. Sb.,181, No. 9, 1207–1219 (1990), English transl.: Math. USSR Sbornik,71, 51–63 (1992).
Thompson J. G., “Finite groups with fixed-point-free automorphisms of prime order,” Proc. Nat. Acad. Sci. U.S.A.,45, 578–581 (1959).
Higman G., “Groups and rings which have automorphisms without non-trivial fixed elements,” J. London Math. Soc. (2),32, 321–334 (1957).
Kreknin V. A. andKostrikin A. I., “Lie algebras with regular automorphisms,” Dokl. Akad. Nauk SSSR,149, No. 2, 249–251 (1963). English transl.: Math. USSR Doklady,4, 355–358 (1963).
Kreknin V. A., “Solvability of Lie algebras with regular automorphisms of finite period,” Dokl. Akad. Nauk SSSR,150, No. 3, 467–469 (1963). English transl.: Math. USSR Doklady,4, 683–685 (1963).
Shumyatsky P., “Involutory automorphisms of finite groups and their centralizers,” Arch. Math. (Basel),71, No. 6, 425–432 (1998).
Makarenko N. Yu., Finite Metabelian Groups Admitting an Automorphism of Prime Order with a Restriction on the Rank of Its Centralizer [Preprint], Inst. Mat. (Novosibirsk), Novosibirsk (1999).
Gorchakov Yu. M., “On existence of abelian subgroups of finite ranks in locally soluble groups,” Dokl. Akad. Nauk SSSR,156, 17–22 (1964). English transl.: Math. USSR, Doklady,5, 591–594 (1964).
Merzlyakov Yu. I., “On locally soluble groups of finite rank,” Algebra i Logika,3, No. 2, 5–16 (1964).
Roseblade J. E., “On groups in which every subgroup is subnormal,” J. Algebra,2, 402–412 (1965).
Kargapolov M. I. andMerzlyakov Yu. I., Fundamentals of the Theory of Groups [in Russian], Springer-Verlag, Berlin etc. (1979).
Gorenstein D., Finite Groups, Chelsea, New York (1968).
Kovács L. G., “On finite soluble groups,” Math. Z.,103, 37–39 (1968).
Additional information
To Yuriî Leonidovich Ershov on the occasion of his 60th birthday.
Supported by the Russian Foundation for Basic Research (Grant 99-01-00576).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 2, pp. 451–469, March–April, 2000.
Rights and permissions
About this article
Cite this article
Khukhro, E.I. Finite soluble and niplotent groups with a restriction on the rank of the centralizer of an automorphism of prime order. Sib Math J 41, 373–388 (2000). https://doi.org/10.1007/BF02674608
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02674608