# Find an isomorphism between U_7 and Z_7

1. Jan 28, 2009

### kathrynag

1. The problem statement, all variables and given/known data

There is an isomorphism of $$U_{7}$$ with $$Z_{7}$$ in which $$\zeta$$=$$e^{(i2\pi}/7$$$$\leftrightarrow$$4. Find the element in $$Z_{7}$$ to which $$\zeta^{m}$$ must correspond for m=0,2,3,4,5, and 6.

2. Relevant equations

3. The attempt at a solution
$$\zeta^{0}$$=0
$$\zeta^{2}$$=4+$$_{7}$$4=1
$$\zeta^{3}$$=$$\zeta^{2}$$$$\zeta^{1}$$=4+$$_{7}$$1=-2

I don't know if I'm doing this right?