On the length of finite factorized groups
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0443-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0443-1 | ||
| 245 | 0 | 0 | |a On the length of finite factorized groups |h [Elektronische Daten] |c [E. Khukhro, P. Shumyatsky] |
| 520 | 3 | |a 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 . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Finite groups |2 nationallicence | |
| 690 | 7 | |a Nonsoluble length |2 nationallicence | |
| 690 | 7 | |a Generalized Fitting height |2 nationallicence | |
| 690 | 7 | |a Factorized group |2 nationallicence | |
| 700 | 1 | |a Khukhro |D E. |u Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia |4 aut | |
| 700 | 1 | |a Shumyatsky |D P. |u Department of Mathematics, University of Brassília, 70910-900, Brasília, DF, Brazil |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1775-1780 |x 0373-3114 |q 194:6<1775 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0443-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0443-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Khukhro |D E. |u Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shumyatsky |D P. |u Department of Mathematics, University of Brassília, 70910-900, Brasília, DF, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1775-1780 |x 0373-3114 |q 194:6<1775 |1 2015 |2 194 |o 10231 | ||