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Archiv der Mathematik

, Volume 82, Issue 5, pp 395–403 | Cite as

The probability of generating a permutation group

  • A. Lucchini
  • F. Morini
Original paper
  • 48 Downloads

Abstract.

It is well known that a permutation group of degree \( n \neq 3 \) can be generated by \( [\frac{n}{2}] \) elements. In this paper we study the asymptotic behavior of the probability of generating a permutation group of degree n with \( [\frac{n}{2}] \) elements. In particular we prove that if n is large enough and \( [\frac{n}{2}] \) elements generate a permutation group G of degree n modulo G G 2, then almost certainly these elements generate G itself.

Mathematics Subject Classification (1991):

20B05 20F69 20P05. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BresciaBresciaItaly

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