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Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where Km is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.
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