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Growth sequences of finite groups III

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

James Wiegold
James Wiegold
Affiliation:
University College Cardiff, Wales
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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.

MSC classification

Secondary: 20D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 142 - 144
Copyright
Copyright © Australian Mathematical Society 1978

References

REFERENCES

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