On the normal index of maximal subgroups in finite groups
The author uses results from primitive group theory to generalize some work of Beidleman and Spencer, Mukherjee, and Mukherjee and Bhattacharya on criteria for solvability, supersolvability, and nilpotency to \(\Pi\)- solvability, \(\Pi\)-supersolvability, and \(\Pi\)-nilpotency. Typical is Theorem 1: Let \(\Pi\) be a set of primes. If finite group G has a \(\Pi\)- solvable maximal subgroup M whose normal index equals its index in G, then G is \(\Pi\)-solvable.
scientific article; zbMATH DE number 4146239