Non-Solvable Graph of a Finite Group and Solvabilizers

Doron Hai-Reuven

Let $G$ be a finite group. For $x\in G$, we define the solvabilizer of $x$ in $G$, denoted $so{l}_G(x)$, to be the set $\{g\in G\mid ⟨g,x⟩$ is solvable$\}$. A group…