ABSTRACT
A study of sets inevitably leads to a study of functions between sets. Similarly, a study of algebraic structures such as semigroups, monoids, or groups entails a study of the functions that preserve the algebraic structure. These functions are known as homomorphisms. If the domain of the group homomorphism in the First Isomorphism Theorem is finite, then the bijection b may be used to count the size of the image. An important application of the First Isomorphism Theorem for Groups is the classical Chinese Remainder Theorem. A. Cayley was an English mathematician who lived from 1821 to 1895. R. Hamming was an American mathematician who lived from 1915 to 1998. L. Euler was a Swiss mathematician, later moving to Russia, who lived from 1707 to 1783.
