A normal subgroup is a subgroup of a group which is invariant under conjugation. Synonyms for the term "normal subgroup" include "invariant subgroup," "invariant factor," and "normal factor." Additionally, "characteristic subgroup" is often used to refer to a normal subgroup which is itself invariant under automorphism of the larger group. Other synonyms that are occasionally used include "normal ideal" and "invariant ideal," although these terms are more commonly used in the context of ring theory. Regardless of the terminology used, the concept of a normal subgroup is fundamental to the study of group theory and plays a crucial role in many areas of mathematics.