A note on test elements for monomorphisms of free groups

2024/08/24 by Dongxiao Zhao, Qiang Zhang, Zhao, Dongxiao +1
Mathematics · Social Sciences · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Japanese History and Culture

paper · pdf · doi:10.48550/arxiv.2408.13449

openalex publication_date 2024/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph.

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