Author

Ohad Sheinfeld

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Preprint Sep 2026

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 $\epsilon>0$ such that for any conjugacy class $...

Ohad Sheinfeld · 1 citation

Preprint Sep 2026

The Robust Thompson's Conjecture for Alternating Groups

We show that there exists a constant $\epsilon>0$ such that if $C$ is a conjugacy class in $A_n$ of size at least $|A_n|^{1-\epsilon}$, then $A_n \setminus \{1\} \subseteq C^2$. This proves the robust version of Thompson's conjecture for the alternating group, conjectured by Shalev (Annals of Math., 2009). Our proof co...

Nathan Keller, Noam Lifshitz, Avichai Marmor et al. · 0 citations