Geodesic
The Quantitative Kurosh Problem
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e42

Voir la notice de l'article provenant de la source Cambridge University Press

We prove a strong quantitative version of the Kurosh Problem, which has been conjectured by Zelmanov, up to a mild polynomial error factor, thereby extending all previously known growth rates of algebraic algebras. Consequently, we provide the first counterexamples to the Kurosh Problem over any field with known subexponential growth, and the first examples of finitely generated, infinite-dimensional, nil Lie algebras with known subexponential growth over fields of characteristic zero.We also widen the known spectrum of the Gel’fand–Kirillov dimensions of algebraic algebras, improving the answer of Alahmadi–Alsulami–Jain–Zelmanov to a question of Bell, Smoktunowicz, Small and Young. Finally, we prove improved analogous results for graded-nil algebras. 
Greenfeld, Be’eri. The Quantitative Kurosh Problem. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e42. doi: 10.1017/fms.2025.1
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