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BOUNDED GENERATION AND SUBGROUP GROWTH

Published online by Cambridge University Press:  18 January 2002

L. PYBER
L. PYBER
Affiliation:
Rényi Institute of the Hungarian Academy of Sciences, P.O.B. 127, H–1364 Budapest, Hungary; pyber@renyi.hu
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Abstract

The author proves in this paper that every profinite group G with polynomial subgroup growth is boundedly generated; that is, it is a product of finitely many procyclic subgroups. This answers a question of P. Zalesskii. By contrast, if G is a boundedly generated group, then the subgroup growth of G is at most nclogn . As a byproduct, a short, elementary proof demonstrates that Aut(Fr) (for r [ges ] 2) and many other related groups are not boundedly generated.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 1 , January 2002 , pp. 55 - 60
Copyright
© The London Mathematical Society 2002

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