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

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

2011-06-08

arxiv.org/abs/1106.1619v2

Mathematics

Group Theory

v2: 32 pages, minor changes, reference added, accepted to International Journal of Algebra and Computation

Scientific paper

10.1142/S0218196712500178

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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