Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.18103 |
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Sommario:
- 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.