An ideal class group is a mathematical concept used in the field of algebra, particularly in the study of number theory. It is a type of group that arises from the ideal class group of a number field, which helps to understand the structure of its ideals. The ideal class group measures how far a given ring of integers is from being a unique factorization domain. In an ideal class group, each element represents an equivalence class of fractional ideals. Two ideals are considered equivalent if their product with a principal ideal is a principal ideal itself. This concept is crucial for studying the properties of algebraic integers and their factorization in rings.