, Volume 16, Issue 4, pp 527–533 | Cite as

Groups with super-exponential subgroup growth

  • L. Pyber
  • A. Shalev


We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.

Mathematics Subject Classification (1991)

primary: 20E07 20E26 secondary: 20B35 20E18 


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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • L. Pyber
    • 1
  • A. Shalev
    • 2
  1. 1.Mathematical InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Institute of MathematicsHebrew UniversityJerusalemIsrael

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