A note on test elements for monomorphisms of free groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916032153649152 |
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| author | Zhao, Dongxiao Zhang, Qiang |
| author_facet | Zhao, Dongxiao Zhang, Qiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on test elements for monomorphisms of free groups Zhao, Dongxiao Zhang, Qiang Group Theory 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. |
| title | A note on test elements for monomorphisms of free groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.13449 |