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arXiv · 2308.16750

The non-two-primes graph of a finite group

Karmele Garatea-Zaballa·Andrea Lucchini
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Abstract

To any finite group $G$, we may associate a graph whose vertices are the elements of $G$ and where two distinct vertices $x$ and $y$ are adjacent if and only if the order of the subgroup $\langle x, y\rangle$ is divisible by at least 3 distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most 5.

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Karmele Garatea-Zaballa, Andrea Lucchini. 2023-08-31. The non-two-primes graph of a finite group. https://arxiv.org/abs/2308.16750

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