Maximal Frattini \(p\)-modules of minimal nonsolvable groups, having cyclic Sylow \(p\)-subgroups
Let \(H\) be a finite group with the Frattini subgroup \(\Phi(H)\) and let \(G=H/\Phi(H)\). Suppose \(\Phi(H)\) is an elementary abelian \(p\)-subgroup for a prime \(p\). The author describes the structure of \(\Phi(H)\) as a \(G\)-module for the cases \(G=\mathrm{PSL}(2,q)\) or \(\mathrm{Sz}(2^ m)\) and a Sylow \(p\)-subgroup of \(G\) is cyclic.
scientific article; zbMATH DE number 3953038