Abstract
In this paper we show that groups, all of whose maximal abelian subgroups are either normal or have a normal complement, are solvable and their degree of solvability is not higher than four. Periodic groups with the above property are locally finite. For a short description of these groups, see [5].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
C. Hopkins, “Finite groups in which conjugate operations are commutative,” Am. J. Math.,51, 35–41 (1929).
W. Burnside, “On groups in which every two conjugate operations are permutable,” Proc. London Math. Soc.,35, 28–37 (1903).
P. G. Kontorovich, “Invariantly coverable groups. I,” Matem. sb.,8, 423–430 (1940).
R. W. Carter, “Nilpotent self-normalizing subgroups and system normalizers,” Proc. London Math. Soc.,12, No. 47, 535–563 (1962).
A. N. Fomin, “On groups all of whose maximal abelian subgroups are either normal or have a normal complement,” Seventh All-Union Colloquium on General Algebra. Abstracts of Communications and Lectures [in Russian] (1965), p. 104.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 39–44, January, 1968.
Rights and permissions
About this article
Cite this article
Fomin, A.N. Periodic groups all of whose maximal abelian subgroups are either normal or have a normal complement. Mathematical Notes of the Academy of Sciences of the USSR 3, 25–27 (1968). https://doi.org/10.1007/BF01386960
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01386960