The First Fundamental Group of a Cyclic Group

Abstract

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.