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On Shalev's Quantitative Version of Thompson's Conjecture
The classical Thompson's conjecture asserts that in any finite nonabelian simple group $G$, there exists a conjugacy class $S$ whose square is equal to the entire group. Shalev (Annals Math., 2009) conjectured that a much stronger quantitative version holds: there exists $ε> 0$ such that for any con
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