Quaternion Group/Group Presentation

Group Presentation of Quaternion Group
The group presentation of the quaternion group is given by:
 * $\Dic 2 = \gen {a, b: a^4 = e, b^2 = a^2, a b a = b}$

Proof
Let $G = \gen {a, b: a^4 = e, b^2 = a^2, a b a = b}$.

It is to be demonstrated that $\Dic 2$ is isomorphic to $G$.

Consider the Cayley table for $\Dic 2$:

We have that:
 * $a^4 = e$
 * $b^2 = a^2$
 * $\paren {a b} a = b$

demonstrating that $\Dic 2$ has the same group presentation as $G$.

Hence the result.