Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T19:31:30.489Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)