# On non-surjective word maps on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$.

@article{Biswas2020OnNW, title={On non-surjective word maps on \$\mathrm\{PSL\}\_\{2\}(\mathbb\{F\}\_\{q\})\$.}, author={Arindam Biswas and Jyoti Prakash Saha}, journal={arXiv: Group Theory}, year={2020} }

Jambor--Liebeck--O'Brien showed that there exist non-proper-power word maps which are not surjective on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$ for infinitely many $q$. This provided the first counterexamples to a conjecture of Shalev which stated that if a two-variable word is not a proper power of a non-trivial word, then the corresponding word map is surjective on $\mathrm{PSL}_2(\mathbb{F}_{q})$ for all sufficiently large $q$. Motivated by their work, we construct new examples of these types of…

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