A class of Frattini-like subgroups of a finite group (Q1183361)

The author extends some results of P. Bhattacharya and N. P. Mukherjee and of X. Guo on the intersections of certain families of maximal subgroups in finite groups from the \(\pi\)-solvable case to the \(\pi\)- separable case. Typical is Theorem 4.2: Let \(G\) be a finite \(\pi\)- separable group. Then \(S_ \pi/O_ \pi(G)\) is supersolvable. (Here \(\pi\) is a set of primes and \(S_ \pi(G)\) is the intersection of all maximal subgroups \(M\) of \(G\) which have composite, \(\pi\)-free indices, or \(G\) if no such \(M\) exists).