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arXiv · 1106.1619

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

Tatiana Bandman·Shelly Garion
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Abstract

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 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.

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Tatiana Bandman, Shelly Garion. 2011-10-10. Surjectivity and equidistribution of the word x^ay^b on PSL(2,q) and SL(2,q). https://doi.org/10.1142/s0218196712500178

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