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Archiv der Mathematik

, Volume 96, Issue 2, pp 115–121 | Cite as

Bounds for the probability of generating the symmetric and alternating groups

  • Attila MarótiEmail author
  • M. Chiara Tamburini
Article

Abstract

We give explicit, asymptotically sharp bounds for the probability that a pair of random permutations of degree n generates either S n or A n and also for the probability that a pair of random even permutations of degree n generates A n . As an application we answer a question of Wiegold in the case of alternating groups.

Mathematics Subject Classification (2000)

Primary 20B30 Secondary 20P05 

Keywords

Symmetric group Alternating group Probability Generation 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.MTA Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.Dipartimento di Matematica e FisicaUniversità Cattolica del Sacro CuoreBresciaItaly

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