• FINITE GROUPS WITH A MAXIMAL NILPOTENT SUBGROUP

Abstract

A solvability condition for finite groups with maximal nilpotent subgroups is given as follows. Let be a finite group and a maximal nilpotent subgroup of . If $P$ is a Sylow 2-subgroup of and every subgroups of of order 2 or 4 is pronormal in , then is solvable.

Keywords: maximal nilpotent subgroups, solvable groups, pronormal subgroups

Subject Classification (2010): 20D10, 20D20.