The probability of generating a finite linear group
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We study the asymptotic behavior of the probability of generating a finite completely reducible linear group G of degree n with [β n] elements. In particular we prove that if β ≧ 3/2 and n is large enough then [β n] randomly chosen elements that generate G modulo O2(G) almost certainly generate G itself.
Mathematics Subject Classification (1991).20G15 20P05
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