Exercise 6.2.1

Proof. We proved in Exercise 6.1.2 that

Every group of order 4 is abelian, and isomorphic to $\mathbb{Z}∕4\mathbb{Z}$ or $\mathbb{Z}∕2\mathbb{Z}\times \mathbb{Z}∕2\mathbb{Z}$.

We note that $G$ has at least 2 elements of order 2, since ${\sigma }^2={\tau }^2=1_L$. This is not the case in $\mathbb{Z}∕4\mathbb{Z}$. Thus

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