Criteria for equidistribution of solutions of word equations on SL(2)

2012/01/25 by Tatiana Bandman, Boris Kunyavskiı̆, Bandman, Tatiana +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1201.5260

openalex publication_date 2012/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study equidistribution of solutions of word equations of the form w(x,y)=g in the family of finite groups SL(2,q). We provide criteria for equidistribution in terms of the trace polynomial of w. This allows us to get an explicit description of certain classes of words possessing the equidistribution property and show that this property is generic within these classes.

Cited by

• ML-invariant and automorphism groups of certain word varieties in SL(2,C)²
• On the asymptotic equidistribution of word values in symmetric groups

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