We study the asymptotic behavior of the probability of generating a finite completely reducible linear group G of degree n with [ba n] elements. In particular we prove that if b > 3/2 and n is large enough then [b n] randomly chosen elements that generate G modulo O^2(G) almost certainly generate G itself.
The probability of generating a finite linear group
LUCCHINI, ANDREA;
2004
Abstract
We study the asymptotic behavior of the probability of generating a finite completely reducible linear group G of degree n with [ba n] elements. In particular we prove that if b > 3/2 and n is large enough then [b n] randomly chosen elements that generate G modulo O^2(G) almost certainly generate G itself.
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