- #1
spacetimedude
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Homework Statement
[itex] ℤ_n → D_n [/itex] sending z modn → [itex]g^z[/itex] where g is rotation by an nth of a turn.
Homework Equations
Group homomorphism imply [itex] θ(g_1*g_2)=θ(g_1)*θ(g_2) [/itex]
The Attempt at a Solution
Before anything, I'd like to know if Group homomorphism imply [itex] θ(g_1+g_2)=θ(g_1)[/itex]x[itex]θ(g_2) [/itex] I've seen [itex] θ(g_1[/itex]x[itex]g_2)=θ(g_1)×θ(g_2) [/itex] and [itex] θ(g_1+g_2)=θ(g_1)+θ(g_2) [/itex] but not [itex] θ(g_1+g_2)=θ(g_1)[/itex]x[itex]θ(g_2) [/itex]. Can the operator * be different on the left and right side?
Attempt:
[itex] θ(z_1+z_2)[/itex]=g[itex]z_1+z_2 modn [/itex]
I'm not sure how to go from here. I'm sure I need to use the fact that [itex]g^n=e[/itex] but I don't know how to proceed.
Any help will be appreciated!
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