Analysis of normality of quotient subgroups on matrices integers modulo prime

Abstract

A set of matrices integers modulo prime forms a finite group. This group has trivial and nontrivial subgroups. The trivial subgroup is normal and for a non-trivial subgroup the normal properties will be investigated. Furthermore, if a nontrivial subgroup is a normal subgroup, then a quotient subgroup can be constructed. This paper discusses the characteristics of normality of quotient subgroup on matrices integers modulo prime. By study of literatures, the order of group play an important role in this quotient subgroup. We derive some characteristics of normality of quotient subgroup. The result is that the order of subgroup determine on the normality of a quotient subgroup.