The First Fundamental Group of a Cyclic Group - Yanita , Aidil Adrianda , Lyra Yulianti (International Journal of Advanced Science and Technology, 2020)
This paper discusses the elements of the first fundamental group of a finite cyclic group. To determines the first fundamental group needed a directed graph. In this case, it uses identity graphs of finite cyclic groups, and these graphs are given directions, and after this referred to as the directed identity graph. First, it is calculated how many directed identity graphs can be generated by the identity graph of the cyclic group. Next, the equivalence classes of closed paths are obtained from the directed identity graph by determining a fixed point. These equivalence classes of closed paths are elements of the first fundamental group. The number of equivalence classes is distinguished by order from the finite cyclic group, i.e., odd, prime, and even orders.