Some results on the solubility graph of a finite group

2023/05/19 by Poozesh, Mina, Zamani, Yousef
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2305.11446

Abstract

Let G be a finite insoluble group with soluble radical R(G). The solubility graph Γ_{\rm S}(G) of G is a simple graph whose vertices are the elements of G∖ 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 Γ_{\rm S}(G).

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