On the diameter of intersection graphs of finite groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911804244885504 |
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| author | Lee, Melissa Rekvényi, Kamilla |
| author_facet | Lee, Melissa Rekvényi, Kamilla |
| contents | The intersection graph $Δ_G$ of a finite group $G$ is a simple graph with vertices the non-trivial proper subgroups of $G$, and an edge between two vertices if their corresponding subgroups intersect non-trivially. These graphs were introduced by Csákány and Pollák in 1969. In this paper we answer two long-standing open questions posed by Csákány and Pollák concerning the diameter of intersection graphs. We prove some necessary conditions for a non-simple group to have an intersection graph of diameter 4. We also construct the first examples of non-simple groups and alternating groups whose intersection graphs have diameter 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the diameter of intersection graphs of finite groups Lee, Melissa Rekvényi, Kamilla Group Theory 05C25, 20E32 The intersection graph $Δ_G$ of a finite group $G$ is a simple graph with vertices the non-trivial proper subgroups of $G$, and an edge between two vertices if their corresponding subgroups intersect non-trivially. These graphs were introduced by Csákány and Pollák in 1969. In this paper we answer two long-standing open questions posed by Csákány and Pollák concerning the diameter of intersection graphs. We prove some necessary conditions for a non-simple group to have an intersection graph of diameter 4. We also construct the first examples of non-simple groups and alternating groups whose intersection graphs have diameter 4. |
| title | On the diameter of intersection graphs of finite groups |
| topic | Group Theory 05C25, 20E32 |
| url | https://arxiv.org/abs/2403.04157 |