The commuting graphs of certain cyclic-by-abelian groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910715141423104 |
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| author | Velten, Timo |
| author_facet | Velten, Timo |
| contents | Let $G$ be a finite, non-abelian group of the form $G = A N$, where $A \leq G$ is abelian, and $N \trianglelefteq G$ is cyclic. We prove that the commuting graph $Γ(G)$ of $G$ is either a connected graph of diameter at most four, or the disjoint union of $|G'| + 1$ complete graphs. These results apply to all finite metacyclic groups, and to groups of square-free order in particular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The commuting graphs of certain cyclic-by-abelian groups Velten, Timo Group Theory Let $G$ be a finite, non-abelian group of the form $G = A N$, where $A \leq G$ is abelian, and $N \trianglelefteq G$ is cyclic. We prove that the commuting graph $Γ(G)$ of $G$ is either a connected graph of diameter at most four, or the disjoint union of $|G'| + 1$ complete graphs. These results apply to all finite metacyclic groups, and to groups of square-free order in particular. |
| title | The commuting graphs of certain cyclic-by-abelian groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.18103 |