The probability of generating a finite classical group

Abstract

Two randomly chosen elements of a finite simple classical group G are shown to generate G with probability →1 as ‖G‖ → ∞. Extensions of this result are presented, along with applications to profinite groups.

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For Jacques Tits on his sixtieth birthday

Research by W.M.K. was supported in part by the NSF and the NSA; and research by A.L. was supported in part by the BSF.

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Kantor, W.M., Lubotzky, A. The probability of generating a finite classical group. Geom Dedicata 36, 67–87 (1990). https://doi.org/10.1007/BF00181465

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Keywords

  • Classical Group
  • Finite Classical Group
  • Simple Classical Group
  • Finite Simple Classical Group