The connectivity of the normalising and permuting graph of a finite soluble group
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929673417523200 |
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| author | Farrell, Eoghan Parker, Chris |
| author_facet | Farrell, Eoghan Parker, Chris |
| contents | We introduce the normalising graph of a group and study the connectivity of the normalising and permuting graphs of a group when the group is finite and soluble. In particular, we classify finite soluble groups with disconnected normalising graph. The main results shows that if a finite soluble group has connected normalising graph then this graph has diameter at most 6. Furthermore, this bound is tight. A corollary then presents the connectivity properties of the permuting graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The connectivity of the normalising and permuting graph of a finite soluble group Farrell, Eoghan Parker, Chris Group Theory Combinatorics 20D We introduce the normalising graph of a group and study the connectivity of the normalising and permuting graphs of a group when the group is finite and soluble. In particular, we classify finite soluble groups with disconnected normalising graph. The main results shows that if a finite soluble group has connected normalising graph then this graph has diameter at most 6. Furthermore, this bound is tight. A corollary then presents the connectivity properties of the permuting graph. |
| title | The connectivity of the normalising and permuting graph of a finite soluble group |
| topic | Group Theory Combinatorics 20D |
| url | https://arxiv.org/abs/2411.19837 |