On surjectivity of word maps on PSL₂

2021/01/29 by Urban Jezernik, Jezernik, Urban, Jonatan Sánchez +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2101.12534

openalex publication_date 2021/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w = [[x^k, y^l], [x^m, yⁿ]] be a non-trivial double commutator word. We show that w is surjective on PSL₂(K), where K is an algebraically closed field of characteristic 0.

Related

• On non-surjective word maps on PSL₂(\mathbbF_q)
• Surjectivity of certain word maps on PSL(2,C) and SL(2,C)
• A Family of surjective word map on SU(2)
• Surjective word maps and Burnsides p^aq^b theorem
• Word maps on perfect algebraic groups