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arXiv · 2202.09563

On the solubilizer of an element in a finite group

Banafsheh Akbari·Costantino Delizia·Carmine Monetta
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Abstract

The solubility graph $\Gamma_S(G)$ associated with a finite group $G$ is a simple graph whose vertices are the elements of $G$, and there is an edge between two distinct vertices if and only if they generate a soluble subgroup. In this paper, we focus on the set of neighbors of a vertex $x$ which we call the solubilizer of $x$ in $G$, $\mathrm{Sol}_G(x)$, investigating both arithmetic and structural properties of this set.

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Banafsheh Akbari, Costantino Delizia, Carmine Monetta. 2022-02-19. On the solubilizer of an element in a finite group. https://doi.org/10.1007/s00009-023-02341-1

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