Probabilistic generation of wreath products on non-abelian finite simple groups

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14 Citations (Scopus)

Abstract

We show that the probability of generating an iterated standard wreath product of non-abelian finite simple groups is positive and tends to 1 as the order of the first simple group tends to infinity. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated. Information depending on the Classification of Finite Simple Groups is used throughout.

Original languageEnglish
Pages (from-to)4753-4768
Number of pages16
JournalCommunications in Algebra
Volume32
DOIs
Publication statusPublished - 2004

Keywords

  • groups
  • generation
  • wreath product
  • probability
  • MAXIMAL-SUBGROUPS
  • EXCEPTIONAL GROUPS
  • CLASSICAL GROUP
  • LIE TYPE
  • AUTOMORPHISM-GROUPS
  • MONSTER
  • ORDERS
  • ODD

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