The SLIN conjecture for special polynomial automorphism groups

Let SAn(K){\rm SA}_n(\mathbb{K}) denote the group of special polynomial automorphisms, and let SLINn(K){\rm SLIN}_n(\mathbb{K}) denote the corresponding subgroup satisfying the special linearization property. SLIN conjecture. If KF2\mathbb{K}\neq\mathbb{F}_2, then

SLINn(K)=SAn(K).{\rm SLIN}_n(\mathbb{K})={\rm SA}_n(\mathbb{K}).

This is presented as a slightly stronger conjecture than the Maubach–Poloni conjecture. The source does not state a resolution, so the conjecture remains open.

Sources & referencesView supporting material

Primary source

Drew Lewis, “Normal subgroups generated by a single polynomial automorphism”, arXiv:1709.04510 (2018).

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