论文标题
在有限组中的元素的溶解度上
On the solubilizer of an element in a finite group
论文作者
论文摘要
与有限组$ g $相关的溶解度图$γ_s（g）$是一个简单的图形，其顶点是$ g $的元素，并且仅当它们生成可溶性子组时，两个不同的顶点之间存在边缘。在本文中，我们专注于顶点$ x $的邻居集，我们称之为$ x $ in $ g $，$ \ mathrm {sol} _g（x）$的溶解度，研究此组的算术和结构属性。
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.
