- #1

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## Homework Statement

## The Attempt at a Solution

I'm very new to this kind of maths, so don't quite know how to get started. If I understood the question at all we have

[tex]g_i \mapsto \phi_i[/tex]

and so I have a homomorphism if I can show that

[tex] \pi(g \cdot g_i) = \pi(g) \circ \pi(g_i) [/tex]

I'm thinking it's trivially injective (might be way off here) because each g maps to a unique element in the symmetric group so there's not much to show.

But to show the homomorphism? Frankly don't have a clue

[tex] j = \phi_g (i)[/tex]

[tex]\pi(g \cdot g_i) = \pi(g_j) = \phi_{g_j}[/tex]

[tex]\pi(g) \circ \pi(g_i) = \phi_g \circ \phi_{g_i}[/tex]

and then I come to a halt. How do I approach this?