Normal Restriction in Finite Groups

Abstract

A subgroup H of a finite group G is called an NR − subgroup (Normal Restriction) if whenever K ⊴ H, then K ^G ∩ H = K, where K ^G is the normal closure of K in G. In this article, we will prove some sufficient conditions for the solvability of finite groups which possess many NR-subgroups. We also prove a criterion for the existence of a normal p-complement in finite groups.

Key Words:

• p-nilpotent
• Solvable

2000 Mathematics Subject Classification:

• Primary 20D10: Secondary 20D05

ACKNOWLEDGMENT

I am grateful to Professor Christopher W. Parker for drawing my attention to the paper of B. Baumann [1].

Notes

Communicated by A. Turull.