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arXiv · 2608.17891

Thompson's Conjecture for Finite Simple Groups of Lie Type over Small Fields

Jun Liao·Lizhong Wang·Jiping Zhang
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Abstract

We prove that every finite simple group of Lie type over a field of order at most 8 contains a conjugacy class whose square is the whole group. Together with the previously established cases, our results complete the proof of Thompson's conjecture. We explicitly construct the required class, address all low-rank identifications, and provide the precise computational certificates used in the exceptional character calculations.

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Jun Liao, Lizhong Wang, Jiping Zhang. 2026-08-18. Thompson's Conjecture for Finite Simple Groups of Lie Type over Small Fields. https://arxiv.org/abs/2608.17891

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