Normal form for free groups and free product of groups

In group theory, the concept of "normal form" can refer to a variety of representations that provide a canonical way to express elements in certain types of groups, particularly free groups and free products of groups. ### Normal Form for Free Groups A **free group** is a group where the elements can be represented as reduced words over a set of generators, with no relations other than those that are necessary to satisfy the group axioms (e.g., inverses for each generator).