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arXiv · 2408.13449

A note on test elements for monomorphisms of free groups

Qiang Zhang·Dongxiao Zhao
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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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Qiang Zhang, Dongxiao Zhao. 2024-08-24. A note on test elements for monomorphisms of free groups. https://arxiv.org/abs/2408.13449

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