Classical groups, probabilistic methods, and the (2, 3)-generation problem

Martin W. Liebeck, Aner Shalev

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


We study the probability that randomly chosen elements of prescribed type in a finite simple classical group G generate G; in particular, we prove a conjecture of Kantor and Lubotzky in this area. The probabilistic approach is then used to determine the finite simple classical quotients of the modular group PSL2(ℤ), up to finitely many exceptions.

Original languageAmerican English
Pages (from-to)77-125
Number of pages49
JournalAnnals of Mathematics
Issue number1
StatePublished - Jul 1996


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