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, SolG(x), investigating both arithmetic and structural properties of this set.
On the solubilizer of an element in a finite group
Delizia, C
;Monetta, C
2023
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, SolG(x), investigating both arithmetic and structural properties of this set.File in questo prodotto:
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