caa a22 4500 60549603X CHVBK 20210128100534.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10231-014-0443-1 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0443-1 On the length of finite factorized groups [Elektronische Daten] [E. Khukhro, P. Shumyatsky] The nonsoluble length $$\lambda (G)$$ λ ( G ) of a finite group $$G$$ 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 $$G$$ G is the least number $$h=h^*(G)$$ h = h ∗ ( G ) such that $$F^*_h(G)=G$$ F h ∗ ( G ) = G , where $$F^*_1(G)=F^*(G)$$ F 1 ∗ ( G ) = F ∗ ( G ) is the generalized Fitting subgroup, and $$F^*_{i+1}(G)$$ F i + 1 ∗ ( G ) is the inverse image of $$F^*(G/F^*_{i}(G))$$ F ∗ ( G / F i ∗ ( G ) ) . It is proved that if a finite group $$G=AB$$ G = A B is factorized by two subgroups of coprime orders, then the nonsoluble length of $$G$$ G is bounded in terms of the generalized Fitting heights of $$A$$ A and $$B$$ B . It is also proved that if, say, $$B$$ B is soluble of derived length $$d$$ d , then the generalized Fitting height of $$G$$ G is bounded in terms of $$d$$ d and the generalized Fitting height of $$A$$ A . Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Finite groups nationallicence Nonsoluble length nationallicence Generalized Fitting height nationallicence Factorized group nationallicence Khukhro E. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia aut Shumyatsky P. Department of Mathematics, University of Brassília, 70910-900, Brasília, DF, Brazil aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1775-1780 0373-3114 194:6<1775 2015 194 10231 https://doi.org/10.1007/s10231-014-0443-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0443-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Khukhro E. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia aut NATIONALLICENCE 700 1- Shumyatsky P. Department of Mathematics, University of Brassília, 70910-900, Brasília, DF, Brazil aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1775-1780 0373-3114 194:6<1775 2015 194 10231