Abstract
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 language | English |
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Article number | 1250017 |
Journal | International Journal of Algebra and Computation |
Volume | 22 |
Issue number | 2 |
DOIs | |
State | Published - 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).
Funding
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). S. Garion is supported by a European Post-doctoral Fellowship (EPDI), during her stay at the Institut des Hautes Études Scientifiques (Bures-sur-Yvette).
Funders | Funder number |
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Israeli Academy of Sciences and Minerva Foundation | |
Ministry of Aliyah and Immigrant Absorption | |
École des hautes études en santé publique |
Keywords
- Special linear group
- finite fields
- trace map
- word map