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On the length of finite factorized groups

Content Provider	Springer Nature Link
Author	Shumyatsky, P. Khukhro, E. I.
Copyright Year	2014
Abstract	The nonsoluble length $$\lambda (G)$$ of a finite group $$G$$ is defined as the minimum number of nonsoluble factors in a normal series each of whose factors either is soluble or is a direct product of non-abelian simple groups. The generalized Fitting height of a finite group $$G$$ is the least number $$h=h^(G)$$ such that $$F^_h(G)=G$$ , where $$F^_1(G)=F^(G)$$ is the generalized Fitting subgroup, and $$F^_{i+1}(G)$$ is the inverse image of $$F^(G/F^*_{i}(G))$$ . It is proved that if a finite group $$G=AB$$ is factorized by two subgroups of coprime orders, then the nonsoluble length of $$G$$ is bounded in terms of the generalized Fitting heights of $$A$$ and $$B$$ . It is also proved that if, say, $$B$$ is soluble of derived length $$d$$ , then the generalized Fitting height of $$G$$ is bounded in terms of $$d$$ and the generalized Fitting height of $$A$$ .
Ending Page	1780
Page Count	6
Starting Page	1775
File Format	PDF
ISSN	03733114
e-ISSN	16181891
Journal	Annali di Matematica Pura ed Applicata
Issue Number	6
Volume Number	194
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-08-28
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized Fitting height Nonsoluble length Finite groups Products of subgroups Factorized group Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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