Definition:Opposite Group

Theorem
Let $\left({G, \circ}\right)$ be a group.

We define a new product $*$ on $G$ by:


 * $\forall a, b \in G: a * b = b \circ a$

The algebraic structure $\left({G, *}\right)$ is called the opposite group to $G$.

Also see

 * Opposite Group is Group, demonstrating that this is indeed a group
 * Definition:Group Antihomomorphism
 * Definition:Opposite Ring