Definition:Group Product

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

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


Sources