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- W2949660624 abstract "The nonsoluble length $lambda(G)$ of a finite group $G$ is defined as the minimum number of nonsoluble factors in a normal series of $G$ each of whose quotients 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 $F^*(G/F^*_{i}(G))$. In the present paper we prove that if $lambda (J)leq k$ for every 2-generator subgroup $J$ of $G$, then $lambda(G)leq k$. It is conjectured that if $h^*(J)leq k$ for every 2-generator subgroup $J$, then $h^*(G)leq k$. We prove that if $h^*(langle x,x^grangle)leq k$ for all $x,gin G$ such that $langle x,x^grangle$ is soluble, then $h^*(G)$ is $k$-bounded." @default.
- W2949660624 created "2019-06-27" @default.
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- W2949660624 date "2016-02-17" @default.
- W2949660624 modified "2023-09-23" @default.
- W2949660624 title "On the length of a finite group and of its 2-generator subgroups" @default.
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- W2949660624 doi "https://doi.org/10.1007/s00574-016-0111-8" @default.
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