Resources
We give links to some of the books and papers which could be useful.
Arora & Singh Two generation of finite simple groups
Shalev Asymptotic Group Theory
Geck; Malle, The character theory of finite groups of Lie type
William Cocke and Meng-Che Ho On the symmetry of images of word maps in groups
Bandman, Garion, Kunyavskiĭ, Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics.
Gordeev, Kunyavskiĭ, Plotkin, Geometry of word equations in simple algebraic groups over special fields.
Kanel-Belov; Kunyavskii; Plotkin, Word equations in simple groups and polynomial equations in simple algebras.
R. Steinberg, Endomorphisms of Linear Algebraic Groups
Amit Kulshrestha, Rijubrata Kundu and Anupam Singh, Asymptotics of the powers in finite reductive groups