Let $G$ be a finite group. The set of all primes dividing $|G|$ is denoted by $π(G)$. The prime graph $Γ(G)$ of $G$ is defined as follows: the vertices are the elements of $π(G)$, and two distinct vertices $p,q$ are joined by an edge if and only if there is an element of order $pq$ in $G$. The authors prove that if $G$ is a finite group such that $Γ(G)=Γ(F_4(q))$, where $q=2^n>2$, then $G$ has a unique nonabelian composition factor and this factor is isomorphic to $F_4(q)$.
Reviewer: Anatoli Kondrat’ev (Ekaterinburg)