Finite groups with hall subnormally embedded Schmidt subgroups

Abstract

A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded.

Keywords:

• Derived subgroup
• finite group
• hall subgroup
• nilpotent subgroup
• subnormal subgroup

2010 MSC:

• 20D10
• 20D20