The expression "g * h * g⁻¹" represents a mathematical operation in group theory, where g is an element of a group, h is another element, and g⁻¹ is the inverse of g. This operation is known as conjugation, and it transforms the element h by the element g. In this context, conjugation can reveal important properties of the group, such as how elements interact with each other. The result of "g * h * g⁻¹" is still an element of the same group, demonstrating that the structure of the group is preserved under this operation.