Surjectivity and equidistribution of the word x^ay^b on PSL(2,q) and SL(2,q)

Tatiana Bandman, Shelly Garion

We determine the positive integers a,b and the prime powers q for which the word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We moreover show that this map…