On surjectivity of word maps on ${\mathrm{PSL}}_2$

Abstract

Let $w=[[x^k,y^l],[x^m,y^n]]$ be a non-trivial double commutator word. We show that $w$ is surjective on ${\mathrm{PSL}}_2(K)$, where $K$ is an algebraically closed field of characteristic $0$.

12 pages