Smallest non-cyclic quotients of the automorphism group of free groups

2021/10/05 by Sudipta Kolay, Kolay, Sudipta
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2110.01779

openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an new, elementary proof of the result that the smallest non-cyclic quotients of automorphism group of free group is the linear group over the field of two elements, and moreover all minimal quotients are obtained by the standard projection composed with an automorphism of the image. This result, originally due to Baumeister-Kielak-Pierro, proves a conjecture of Mecchia-Zimmermann.

Citations

• On minimal finite quotients of outer automorphism groups of free groups

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