Abstract
It is proved that, if\(\mathfrak{F} = \mathfrak{M}\mathfrak{H}\) is a singly generated composition formation, where\(\mathfrak{H} \ne \mathfrak{F}\), then\(\mathfrak{M}\) is a composition formation.
Similar content being viewed by others
References
W. Gaschutz, “Zur Theorie der endlichen auflosbaren Gruppen,”Math. Z.,80, No. 4, 300–305 (1963).
L. A. Shemetkov, “The product of formations,”Dokl. Akad. Nauk BSSR,28, No. 2, 101–103 (1984).
V. A. Vedernikov, “Local formations of finite groups,”Mat. Zametki [Math. Notes],46, No. 3, 32–37 (1989).
N. T. Vorob’ev, “Factorizations of nonlocal formations of finite groups,” in:Problems in Algebra [in Russian], Vol. 5, Universitetskoe Izd., Minsk (1990), pp. 21–24.
A. N. Skiba, “On nontrivial factorizations of one-generated local formations of finite groups,” in:Proc. Intern. Conf. Algebra Dedicated to the Memory of A. I. Mal’cev (Novosibirsk, August 21–26, 1989), Amer. Math. Soc., Providence (R.I.) (1992), pp. 363–374.
Kourovka Notebook. Unsolved Problems in Group Theory [in Russian], Twelfth edition, Novosibirsk (1992).
L. A. Shemetkov, “Graduated formations of groups,”Mat. Sb. [Math. USSR-Sb.],94, No. 4, 628–648 (1974).
L. A. Shemetkov, “Two trends in the development of the theory of nonsimple finite groups,”Uspekhi Mat. Nauk [Russian Math. Surveys],30, No. 2, 179–198 (1975).
K. Doerk and T. Hawkes,Finite Soluble Groups, Walter de Gruyter, Berlin-New York (1992).
A. N. Skiba and L. A. Shemetkov, “Minimal composition screen of a composition formation,” in:Problems in Algebra [in Russian], Vol. 7, Izd. Gomel. Univ., Gomel (1992), pp. 39–43.
L. A. Shemetkov,Formations of Finite Groups [in Russian], Nauka, Moscow (1978).
L. A. Shemetkov and A. N. Skiba,Formations of Algebraic Systems [in Russian], Nauka, Moscow (1989).
M. M. Kargapolov and Yu. I. Merzlyakov,Foundations of the Theory of Groups [in Russian], Nauka, Moscow (1972).
A. N. Skiba and L. A. Shemetkov, “Hereditarily indecomposable formations of groups,”Dokl. Akad. Nauk BSSR,33, No. 7, 581–583 (1989).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 389–395, March, 1999.
Rights and permissions
About this article
Cite this article
Skiba, A.N. Factorizations of composition formations. Math Notes 65, 326–330 (1999). https://doi.org/10.1007/BF02675074
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02675074