Quasirecognition by prime graph of \(F_4(q)\) where \(q=2^n>2\).
Let \(G\) be a finite group. The set of all primes dividing \(|G|\) is denoted by \(\pi(G)\). The prime graph \(\Gamma(G)\) of \(G\) is defined as follows: the vertices are the elements of \(\pi(G)\), 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 \(\Gamma(G)=\Gamma(F_4(q))\), where \(q=2^n>2\), then \(G\) has a unique nonabelian composition factor and this factor is isomorphic to \(F_4(q)\).
scientific article; zbMATH DE number 5872786
scientific article