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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We determine the integers a, b ≥ 1 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.

Original languageEnglish
Article number1250017
JournalInternational Journal of Algebra and Computation
Issue number2
StatePublished - Mar 2012

Bibliographical note

Funding Information:
T. Bandman is supported in part by Ministry of Absorption (Israel), Israeli Academy of Sciences and Minerva Foundation (through the Emmy Noether Research Institute of Mathematics).

Funding Information:
S. Garion is supported by a European Post-doctoral Fellowship (EPDI), during her stay at the Institut des Hautes Études Scientifiques (Bures-sur-Yvette).


  • Special linear group
  • finite fields
  • trace map
  • word map


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