Two regular unipotent generation conjecture for quasisimple groups of Lie type

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Let GG be a quasisimple finite group of Lie type, and exclude the case G=SL2(q)G=SL_2(q) with qq even.

Two regular unipotent generation conjecture. Then GG is generated by two regular unipotent elements.

This is a broader formulation concerning quasisimple, rather than only simple, finite groups of Lie type. It does not require the two regular unipotent elements to be conjugate; the paper’s surrounding discussion places it among questions about generation by special element classes.

References

Primary source

M. A. Pellegrini and A. E. Zalesski, “Minimal generation of finite simple groups of Lie type by regular unipotent elements”, arXiv:2511.12683 (2025).

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