A proof of Cauchy theorem by action of group
Xianhui Yang, Yanlin He · 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022) · 2022
Group theory is one of the most important aspects in modern science, mathematics, statistics, and computer technology. It was discovered in the nineteenth century in the context of delivering algebraic expression solutions. The group was defined precisely as the set of all permutations of an algebraic statement's roots that satisfy the condition that any two of these permutations belong to the set. This paper defines finite group actions as well as infinite group actions and provides examples. We reviewed some essential features of group action in this study. A comprehensive demonstration of the Cauchy theorem was also provided as an application of group action theory. Cauchy's theorem is a theoretic statement that claims that elements of all conceivable prime orders exist in a finite group.