From Thompson to Baer-Suzuki: a sharp characterization of the solvable radical

Nikolai Gordeev, Fritz Grunewald, Boris Kunyavskii +1

We prove that an element $g$ of prime order $>3$ belongs to the solvable radical $R(G)$ of a finite (or, more generally, a linear) group if and only if for every $x\in G$ the subgr…