Group homomorphism

A group homomorphism is a mathematical concept that describes a consistent way to relate two groups. Think of a group as a collection of elements combined with an operation, like addition or multiplication. A homomorphism is a function that takes elements from one group and transforms them into another, while preserving the group structure. This means if you combine two elements in the first group, the result after applying the homomorphism will be the same as combining their images in the second group. It helps scientists and mathematicians understand relationships between different algebraic systems.