Definition:Isomorphism Class (Algebraic Structures)

Definition
Let $\struct {S, \circ}$ be an algebraic structure.

Let $\phi: S \to S$ be an isomorphism on $\struct {S, \circ}$

Let $x \in S$.

Let $\cong$ denote isomorphism.

The isomorphism class of $x$ is the set of elements of $\struct {S, \oplus}$ such that $x \cong y$.