Technical report: classification of groups of order 16 / Nur Nabihah Mohd Saber, Syafieza Saidin and Nur Zahira Mohamed Zahir

Abstract algebra, also known as modem algebra is a broad division of mathematics. It is the set of advanced topics of algebra that deal with abstract algebraic structures of various sets such as real numbers, complex number, vector spaces and matrices rather than rules and procedures for manipulating their individual elements. The important of these structures are group, ring and field. This research has been conducted to classify the group of order 16 as it is always obtained as a special case of sophisticated theory of p-groups. Group is defined as a set G which is closed under the binary operation while a group is called a p-group if it has the order of power of prime. To prove that there is no more group of order n is the problem that has been arisen during this research. To make the classification of groups easier and also as the solution to the problem, the idea of group presentation is used. Presentation of group is one of the methods of defining a group. The groups are formed by giving a set of generators and certain equations which are satisfied by the generators. The objectives for this project are identifying all the groups of order 16 and determining their abelian groups. At the end of this research on classification of groups of order 16, 14 groups has been obtained which the first five is abelian and the rest of it is non-abelian.