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BOUNDED GENERATION AND SUBGROUP GROWTH
Published online by Cambridge University Press: 18 January 2002
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.
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- © The London Mathematical Society 2002
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