Density of quotient orders in groups and applications to locally-transitive graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929555406585856 |
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| author | Conder, Marston Verret, Gabriel Young, Darius |
| author_facet | Conder, Marston Verret, Gabriel Young, Darius |
| contents | We prove that the set of orders of finite quotients of a finitely generated group has natural density 0, 1/2 or 1, and characterise when each of these cases occurs. We apply this to show that the sets of orders of various families of symmetric graphs have natural density 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density of quotient orders in groups and applications to locally-transitive graphs Conder, Marston Verret, Gabriel Young, Darius Group Theory Combinatorics We prove that the set of orders of finite quotients of a finitely generated group has natural density 0, 1/2 or 1, and characterise when each of these cases occurs. We apply this to show that the sets of orders of various families of symmetric graphs have natural density 0. |
| title | Density of quotient orders in groups and applications to locally-transitive graphs |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2410.17828 |