Abstract
In the paper we list all solvable normally hereditary local formationsF such that in any finite groupG the product of every commutingF-subnormal subgroups ofG is aF-subnormal subgroup of the groupG.
Similar content being viewed by others
References
H. Wielandt, “Eine Verallgemeinerung der invarianten Untergruppen,”Math. Z.,45, 209–244 (1939).
L. A. Shemetkov,Formations of Finite Groups [in Russian], “Nauka,” Moscow (1978).
A. F. Vasil'ev, S. F. Kramarnikov, and V. N. Semenchuk, “Lattices of subgroups of finite groups,” in:Conference of Belarus Mathematicians [in Russian], Grodno (1992), p. 10.
V. N. Semenchuk, “Minimal non-188-01-groups,”Algebra i Logika [Algebra and Logic],18, No. 3, 348–382 (1979).
V. N. Semenchuk, “Description of finite solvable minimal non-188-02-groups for an arbitrary totally local formation 188-03,”Mat. Zametki [Math. Notes],43, No. 4, 452–459 (1988).
A. F. Vasil'ev, “The maximal hereditary subformation of a local formation,”Voprosy Algebry (Minsk University), No. 5, 39–45 (1990).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 261–266, February, 1996.
Rights and permissions
About this article
Cite this article
Semenchuk, V.N. SolvableF-radical formations-radical formations. Math Notes 59, 185–188 (1996). https://doi.org/10.1007/BF02310958
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02310958