On non-surjective word maps on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$
Group Theory
2020-12-03 v1 Number Theory
Abstract
Jambor--Liebeck--O'Brien showed that there exist non-proper-power word maps which are not surjective on for infinitely many . 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 for all sufficiently large . Motivated by their work, we construct new examples of these types of non-surjective word maps. As an application, we obtain non-surjective word maps on the absolute Galois group of .
Cite
@article{arxiv.2012.01408,
title = {On non-surjective word maps on $\mathrm{PSL}_{2}(\mathbb{F}_{q})$},
author = {Arindam Biswas and Jyoti Prakash Saha},
journal= {arXiv preprint arXiv:2012.01408},
year = {2020}
}