Analysis Of Normality Of Quotient Subgroup On Matrices Integers Modulo Prime
Ibnu Hadi (a*), Selly Anastassia Amellia Kharis (a)
a) Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta, Jalan Rawamangun Muka, Jakarta 13220, Indonesia
*ibnu_unj[at]yahoo.co.id
Abstract
A set of matrices integers modulo prime can form a finite group. This group has trivial and non-trivial subgroups. The trivial subgroup is normal clearly and for a non-trivial subgroup the normal properties will be investigated. Furthermore, if a non-trivial 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. A group is constructed by matrices integers modulo prime. Here we considered some properties of this group. The order of group play an important role in this quotient subgroup. By this concept, we derive some result of normality of quotient subgroup. From this paper, it was found that the subgroup order had an effect on the normality of a quotient subgroup.
Keywords: Order of Group, Normality of Quotient Subgroup, Matrices Integers Modulo Prime
Topic: Mathematics