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Growth sequences of finite groups V

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

D. Meier  and
James Wiegold
D. Meier
Affiliation:
Mathematics Institute, University of Warwick, Coventry, England
James Wiegold
Affiliation:
University College, Cardiff, Wales
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Abstract

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A short and easy proof that the minimum number of generators of the nth direct power of a non-trival finite group of order s having automorphism group of order a is more than logsn + logsa, n > 1. On the other hand, for non-abelian simple G and large n, d(Gn) is within 1 + e of logsn + logsa.

MSC classification

Secondary: 20D60: Arithmetic and combinatorial problems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 374 - 375
Copyright
Copyright © Australian Mathematical Society 1981

References

Hall, P. (1936), ‘The Eulerian functions of a group,’ Quart. J. Math. Oxford Ser. 7, 134–151.CrossRefGoogle Scholar
Wiegold, James (1974), ‘Growth sequences of finite groups,’ J. Austral. Math. Soc. 17, 133–141.CrossRefGoogle Scholar
Wiegold, James (1980), ‘Growth sequences of finite groups IV,’ J. Austral. Math. Soc. Ser. A 29, 14–16.CrossRefGoogle Scholar