Abstract
In this paper we describe all abelian groups which can be expanded as the direct product of cyclic subgroups which have regular automorphisms of given prime order and also find the necessary and sufficient conditions for the existence of regular semiautomorphisms of prime order for metabelian groups the orders of the elements of which are bounded as a set.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J. G. Thompson, “Finite groups with fixed-point free automorphisms of prime order,” Proc. Nat. Acad. Sci. USA,45, No. 4, 578–581 (1959).
F. Hoffman, “Nilpotent height of finite groups admitting fixed-point free automorphisms,” Math. Z.,85, 260–267 (1964).
F. Gross, “Some remarks on groups admitting a fixed-point free automorphism,” Canad. J. Math.,20, No. 6, 1300–1307 (1968).
S. V. Larin and N. V. Loiko, “Semiisomorphisms of abelian groups without torsion,” Sibirsk. Matem. Zh.,52, No. 2, 293–297 (1966).
S. V. Larin, “Semiisomorphisms of periodic abelian groups,” Sibirsk. Matem. Zh.,52, No. 2, 298–306 (1966).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 12, No. 6, pp. 727–738, December, 1972.
Rights and permissions
About this article
Cite this article
Glukhov, M.M., Larin, S.V. Abelian and metabelian groups with regular automorphisms and semiautomorphisms. Mathematical Notes of the Academy of Sciences of the USSR 12, 876–881 (1972). https://doi.org/10.1007/BF01156048
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01156048