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arXiv · 2305.11446

Some results on the solubility graph of a finite group

Mina Poozesh·Yousef Zamani
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Abstract

Let $G$ be a finite insoluble group with soluble radical $ R(G)$. The solubility graph $\Gamma_{\rm S}(G)$ of $G$ is a simple graph whose vertices are the elements of $G\setminus R(G) $ and two distinct vertices $x$ and $y$ are adjacent if and only if they generate a soluble subgroup of $G$. In this paper, we investigate the several properties of the solubility graph $\Gamma_{\rm S}(G)$.

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Mina Poozesh, Yousef Zamani. 2023-05-19. Some results on the solubility graph of a finite group. https://arxiv.org/abs/2305.11446

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