A note on test elements for monomorphisms of free groups
arXiv:2408.13449
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.
8 pages, 3 figures