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1 results

  • THE FINITE IMAGES OF FINITELY GENERATED GROUPS

  • DAN SEGAL
  • Journal:
    Proceedings of the London Mathematical Society / Volume 82 / Issue 3 / May 2000
    Published online by Cambridge University Press:
    20 August 2001, pp. 597-613
    Print publication:
    May 2000

  • Given any sequence of non-abelian finite simple primitive permutation groups $(S_{n})$, we construct a finitely generated group $G$ whose profinite completion is the infinite permutational wreath product $\ldots S_{n}\wr S_{n-1}\wr\ldots\wr S_{0}$. It follows that the upper composition factors of$G$ are exactly the groups $S_{n}$. By suitably choosing the sequence $(S_{n})$ we can arrange that $G$ has any one of a continuous range of slow,non-polynomial subgroup growth types. We also construct a $61$-generator perfect group that has every non-abelian finite simple group as a quotient. 2000 Mathematics Subject Classification: 20E07, 20E08, 20E18, 20E32.