A Note on the Normal Index and thec-Section of Maximal Subgroups of a Finite Group

Abstract

LetMbe a maximal subgroup of finite groupG. For each chief factorH/KofGsuch thatK≤MandG=MH, we called the order ofH/Kthe normal index ofMandM∩H/Ka section ofMinG. Using the concepts of normal index andc-section, we obtain some new characterizations ofp-solvable, 2-supersolvable, andp-nilpotent.