Special Applications of Cyclic Groups

Abstract

Cyclic groups are common in our everyday life. A cyclic group is a group with an element that has an operation applied that produces the whole set. A cyclic group is the simplest group. A cyclic group could be a pattern found in nature, for example in a geometric pattern we draw ourselves. Cyclic groups can also be thought of as rotations, if we rotate an object enough time we will eventually return to the original position. In this research paper we explore further applications of cyclic groups in number theory like division algorithm and Chinese remainder theorem and other applications including chaos theory, 12-hour clock, modular system, bell ringing, linear codes. If someone can recognize a cyclic group, they could use the generator to find the fastest simple circuit for use in other real-world applications and in pure mathematics.