March 13, 2024Open Access

Thompson's Conjecture for Large Unitary Groups

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Abstract

We prove that every simple unitary group S of sufficiently large order satisfies Thompson's conjecture, that is, S contains a conjugacy class C such that C² = S. The proof relies on exponential character bounds recently obtained in arXiv: 1708. 03844 and LT3, and a refinement that gives a sharp asymptotic for character ratios in Lie-type groups of type A.

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Larsen et al. (Wed,) studied this question.

synapsesocial.com/papers/68e74464b6db6435876be19e https://doi.org/https://doi.org/10.48550/arxiv.2403.09047

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