It is well known that a permutation group of degree $ n neq 3 $ can be generated by $ [frac{n}{2}] $ elements. In this paper we study the asymptotic behavior of the probability of generating a permutation group of degree n with $ [frac{n}{2}] $ elements. In particular we prove that if n is large enough and $ [frac{n}{2}] $ elements generate a permutation group G of degree n modulo G ‘ G 2, then almost certainly these elements generate G itself.
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