Abstract:

The structure of groups plays an important role in the study of the nature of the groups. We examine some basic properties and structural characteristics of the dihedral group of degree n, where n is a natural number, by group-theoretic approach. We begin the exploration by providing a foundational understanding of dihedral groups, elucidating their definitions and essential properties. Furthermore, we investigated the algebraic and geometric aspects of these groups, highlighting their role in describing symmetries of n-gons and other mathematical entities. Special attention is given to the distinctive features that differentiate dihedral groups from other algebraic structures. The analytic expressions for the order of subgroups are obtained and the commutativity investigated. The groups are all represented for further analysis and applications.