Normal subgroup

A normal subgroup is a special subset within a larger group in mathematics, particularly in algebraic structures called groups. It has two main qualities: first, it behaves consistently when you combine it with any element of the larger group (you can "multiply" elements from the subgroup with any element from the whole group, and the result stays within the subgroup). Second, it allows the entire group to be broken down into smaller, well-structured parts called quotient groups. Think of it as a “balanced core” within the group that helps us understand and analyze the group's overall structure.