2014/05/08 by E. I. Khukhro, Khukhro, E. I., Pavel Shumyatsky +1
Engineering · Mathematics · #20D40 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1405.1899
openalex publication_date 2014/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The nonsoluble length λ(G) of a finite group G is defined as the number of nonsoluble factors in a shortest normal series each of whose factors either is soluble or is a direct product of nonabelian 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.