Bounds for the probability of generating the symmetric and alternating groups

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.

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Correspondence to Attila Maróti.

Additional information

The research of A. Maróti was supported by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme, by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by OTKA NK72523.

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Maróti, A., Chiara Tamburini, M. Bounds for the probability of generating the symmetric and alternating groups. Arch. Math. 96, 115–121 (2011). https://doi.org/10.1007/s00013-010-0216-z

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Mathematics Subject Classification (2000)

  • Primary 20B30
  • Secondary 20P05

Keywords

  • Symmetric group
  • Alternating group
  • Probability
  • Generation