The impact of the solubilizer of an element on the structure of a finite group

Abstract

Let $G$ be a finite group, and let $x$ be an element of $G$. Denote by $\Sol_G(x)$ the set of all $y\in G$ such that the group generated by $x$ and $y$ is soluble. We investigate the influence of $\Sol_G(x)$ on the structure of $G$.

9 pages, research paper