On Generalized Norms of Finite Groups

Abstract

Let ℱ be a subgroup-closed formation and let G be a finite group. Then we definite N_ℱ(G) as the intersection of the normalizers of the ℱ-residuals of all subgroups of G. The main aim of this article is to show the influence of the embedding of this subgroup in the group structure.

Key Words:

• ℱ-hypercentre
• ℱ-residual
• Normalizer

2010 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

The authors would like to thank the referee for his/her valuable suggestions and useful comments contributed to the final version of this article.