A note on test elements for monomorphisms of free groups
Group Theory
2026-05-22 v2
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.
Keywords
Cite
@article{arxiv.2408.13449,
title = {A note on test elements for monomorphisms of free groups},
author = {Dongxiao Zhao and Qiang Zhang},
journal= {arXiv preprint arXiv:2408.13449},
year = {2026}
}
Comments
8 pages, 3 figures