Geodesic
A nonsimple criterion for finite factorized groups
Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 94-95.

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In the study of factorizable groups the authors consider some natural restrictions on the factors. Ito Theorem about two-step solubility of a finite group which is factorized by abelian subgroups, and Kegel-Wielandt Theorem about solubility of a finite group which is a product of two nilpotent subgroups are the classical examples in this trend. We should also note that L.S. Kazarin have obtained validity of the hypothesis of S.A. Chunikhin about non-simplicity of a finite group which is factorized by subgroups with nontrivial center.
Keywords: finite group, simple nonabelian group, factorized group. 
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V. N. Tyutyanov; V. A. Tyutyanova. A nonsimple criterion for finite factorized groups. Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 94-95. http://geodesic.mathdoc.fr/item/PFMT_2012_3_a16/

[1] L. S. Kazarin, “Product of two solvable subgroups”, Comm. Algebra, 14:6 (1986), 1001–1066 | DOI | MR | Zbl

[2] J. H. Conway et al., Atlas of finite groups, Clarendon Press, London, 1985, 252 pp. | MR | Zbl

[3] N. Ito, “On the factorizations of the linear fractional groups $LF(2,p^n)$”, Acta Scient. Math., 15 (1953), 79–84 | MR | Zbl