Geodesic
Jordan Property for the Cremona Group over a Finite Field
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 298-310

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We show that the Cremona group of rank $2$ over a finite field is Jordan, and provide an upper bound for its Jordan constant which is sharp when the number of elements in the field is different from $2$, $4$, and $8$. 
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     author = {Yuri G. Prokhorov and Constantin A. Shramov},
     title = {Jordan {Property} for the {Cremona} {Group} over a {Finite} {Field}},
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     year = {2023},
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Yuri G. Prokhorov; Constantin A. Shramov. Jordan Property for the Cremona Group over a Finite Field. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 298-310. http://geodesic.mathdoc.fr/item/TM_2023_320_a12/