Khukhro, Evgeny and Shumyatsky, P. (2015) On the length of finite factorized groups. Annali di Matematica Pura ed Applicata, 194 (6). pp. 17751780. ISSN 03733114
Documents 


PDF
__ddat02_staffhome_jpartridge_14annalikhushu.pdf  Whole Document Restricted to Repository staff only 389kB  

PDF
15573 khushu141.pdf  Whole Document 295kB 
Item Type:  Article 

Item Status:  Live Archive 
Abstract
The nonsoluble length λ(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 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 .
Keywords:  Factorized group, Finite group, Generalised Fitting height, Nonsoluble length, bmjgoldcheck, NotOAChecked 

Subjects:  G Mathematical and Computer Sciences > G100 Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
Related URLs:  
ID Code:  15573 
Deposited On:  28 Oct 2014 12:02 
Repository Staff Only: item control page