On the surjectivity of Engel words on \(PSL(2,q)\)

DOI10.4171/GGD/162zbMath1261.14010arXiv1008.1397MaRDI QIDQ454398

Shelly Garion, Tatiana Bandman, Fritz J. Grunewald

Publication date: 1 October 2012

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.1397

zbMATH Keywords

finite fieldsperiodic pointstrace mapspecial linear grouparithmetic dynamicsEngel words

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Simple groups: alternating groups and groups of Lie type (20D06) Varieties over finite and local fields (11G25) Arithmetic dynamics on general algebraic varieties (37P55) Dynamical systems over finite ground fields (37P25)

Related Items (11)

Word equations in simple groups and polynomial equations in simple algebras. ⋮ Word maps with constants on symmetric groups ⋮ On non-surjective word maps on \(\mathrm{PSL}_2(\mathbb{F}_q)\) ⋮ Iterated identities and iterational depth of groups ⋮ Criteria for equidistribution of solutions of word equations on \(\mathrm{SL}(2)\). ⋮ Word maps on perfect algebraic groups ⋮ Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. ⋮ Evaluations of noncommutative polynomials on algebras: methods and problems, and the L'vov-Kaplansky conjecture ⋮ Surjectivity of certain word maps on \(\mathrm{PSL}(2,\mathbb {C})\) and \(\mathrm{SL}(2,\mathbb {C})\) ⋮ On Engel words on simple algebraic groups. ⋮ Geometry of word equations in simple algebraic groups over special fields

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