Residual finite simplicity of Aut(F2)\mathrm{Aut}(F_2)

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Let F2F_2 be the free group on two generators. A group is fully residually finite simple if, for every finite subset of its nontrivial elements, there is a homomorphism to a finite simple group whose restriction to that subset is injective. Residual finite simplicity conjecture. Aut(F2)\mathrm{Aut}(F_2) is fully residually finite simple. The paper presents this as a strengthened version of its theorem on characteristic finite simple quotients and expects it to imply strong separation of finite subsets by finite simple quotients.

References

Primary source

Liam Hanany, “The Yang-Baxter Equation and Characteristic Finite Simple Quotients of the Free Group of Rank 2”, arXiv:2510.03210 (2025).

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