On quasinormal subgroups

• Main Authors: Chua, Katherine Ong, Lim, Annabelle Ong
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Quasigroups; Groups, Theory of; Finite groups
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16245
• Institution: De La Salle University

This paper presents to the undergraduate students a new concept on Group Theory called quasinormal subgroup. This generalization of normal subgroups was introduced by Oystein Ore in his article Structures and Group Theory I. Every normal subgroup is a quasinormal subgroup. The converse however is not true. This was shown in the article written by Dean Hickerson, Sherwin Stein and Kenya Yamaoka entitled When Quasinormal Implies Normal, which was the basic reference of this paper.This paper discusses some of the differences between normal and quasinormal subgroups. Some sufficient conditions so that quasinormal subgroups are normal are given in some theorems proved in this paper. Examples of quasinormal subgroups which are not normal and which are normal are also provided in this paper.