Growth sequences of finite groups III

Journal of the Australian Mathematical Society

James Wiegold¹ 

关键词: 20 D 99;   

DOI  :  10.1017/S1446788700038726

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let G be a finite group with d(G) = α, d(G/G′) = β≥1. If G has non-abelian simple images, let s denote the order of a smallest such image. Then d(Gn) = βn provided that βn≥α + 1 + log8n. If all simple images of G are abelian, then d(Gn) = βn provided that βn≥α. If G is non-trivial and perfect, with s again denoting the order of a smallest non-abelian simple image, then d(Gsn)≼d(G) + n for all n≥0. These results improve on results in previous papers with similar titles.

【 授权许可】

Unknown