The concept of a generalized wreath product of permutation m-groups is introduced, and it is proved that an m-transitive permutation group embeds into a generalized wreath product of its primitive components.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Giraudet and J. Rachunek, “Varieties of half lattice-ordered groups of monotonic permutations of chains,” Czech. Math. J., 49, No. 4, 743-766 (1999).
A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
V. M. Kopytov and N. Ya. Medvedev, The Theory of Lattice-Ordered Groups, Kluwer, Dordrecht (1994).
V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).
A. V. Zenkov, “On congruences of m-groups,” Sib. Math. J., 54, No. 6, 1018-1022 (2013).
A. V. Zenkov and O. V. Isaeva, “Two questions in the theory of m-groups,” Sib. Math. J., 55, No. 6, 1042-1044 (2014).
V. M. Kopytov and J. Rachunek, “The greatest proper variety of m-groups,” Algebra and Logic, 42, No. 5, 349-355 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Algebra i Logika, Vol. 58, No. 2, pp. 167-178, March-April, 2019.
Rights and permissions
About this article
Cite this article
Zenkov, A.V., Isaeva, O.V. Generalized Wreath Products of m-Groups. Algebra Logic 58, 115–122 (2019). https://doi.org/10.1007/s10469-019-09530-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10469-019-09530-6