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SURJECTIVITY AND EQUIDISTRIBUTION OF THE WORD x(a)y(b) ON PSL(2, q) AND SL(2, q)

Author:
Bandman, Tatiana  Garion, Shelly  


Journal:
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION


Issue Date:
2012


Abstract(summary):

We determine the integers a, b >= 1 and the prime powers q for which the word map w(x, y) = x(a)y(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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