On the solubilizer of an element in a finite group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866914125104283648 |
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| author | Akbari, Banafsheh Delizia, Costantino Monetta, Carmine |
| author_facet | Akbari, Banafsheh Delizia, Costantino Monetta, Carmine |
| contents | The solubility graph $Γ_S(G)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09563 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the solubilizer of an element in a finite group Akbari, Banafsheh Delizia, Costantino Monetta, Carmine Group Theory 20D10, 05C25, 20D60 The solubility graph $Γ_S(G)$ 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. |
| title | On the solubilizer of an element in a finite group |
| topic | Group Theory 20D10, 05C25, 20D60 |
| url | https://arxiv.org/abs/2202.09563 |