A note on test elements for monomorphisms of free groups
Dongxiao Zhao, Qiang Zhang

TL;DR
This paper provides a geometric condition using Whitehead graphs and Cayley graph actions to identify test elements for monomorphisms in free groups.
Contribution
It introduces a new geometric criterion for constructing test elements in free groups, expanding understanding of their automorphism properties.
Findings
Provides a sufficient geometric condition for test elements
Uses Whitehead graph and Cayley graph actions in the construction
Enhances methods for analyzing monomorphisms in free groups
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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Taxonomy
TopicsGeometric and Algebraic Topology · Japanese History and Culture
