SURJECTIVITY AND EQUIDISTRIBUTION OF THE WORD xaybON PSL (2, q) AND SL (2, q)
TATIANA BANDMAN, SHELLY GARION · International Journal of Algebra and Computation · 2011
We determine the integers a, b ≥ 1 and the prime powers q for which the word map w(x, y) = xaybis surjective on the group PSL (2, q) (and SL (2, q)). We moreover show that this map is almost equidistributed for the family of groups PSL (2, q) (and SL (2, q)). Our proof is based on the investigation of the trace map of positive words.