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

From papers

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.

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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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