On Frattini extensions of the projective special linear group (Q1177549)

Let \(G^ \varphi\) be the image of a finite group \(G\) under a homomorphism \(\varphi\) with the kernel \(\text{ker }\varphi = \Phi\) lying in the Frattini subgroup \(\Phi(G)\) of the group \(G\). In this case we call \(G\) a Frattini extension of the group \(G^ \varphi\). We construct Frattini extensions of the groups \(\text{PSL}(n,p^ f)\) except for the case \(p = 2\).