Question

Recall that $\mathbb{Z}_{7}^{\times }$ is the group of units in $\mathbb{Z}_{7}$, with operation given by multiplication.

Consider the function $\phi:\mathbb{Z}_{6}\rightarrow \mathbb{Z}_{7}^{\times }$ defined by $\phi([n]_{6})=[a^{n}]_{7}$ . Show that this function is well-defined.

Show that $\phi$ is an isomorphism.

Answer 1

Here to show that phi function is isomorphism for this we show that it is homomorphism ,one to one and onto.all property satisfies .Answer is below thank you.

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