# Definition:Group Product

## Definition

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

The operation $\circ$ is referred to in this context as the group product or just product.

## Examples of Operations on Group Product

### Example: $b x a^{-1} = a^{-1} b$

$b x a^{-1} = a^{-1} b$

### Example: $a x a^{-1} = e$

$a x a^{-1} = e$

### Example: $a x a^{-1} = a$

$a x a^{-1} = a$

### Example: $a x b = c$

$a x b = c$

### Example: $b a^{-1} x a b^{-1} = b a$

$b a^{-1} x a b{^-1} = b a$