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 $G$.Comment: 9 pages, research pape