Let x=e^(2∏/13i), a primitive 13th root of unity.

Find a subfield K of Q(X) with (Q(x):K)=3.

Find a subfield L of Q(X) with (Q(x):L)=4.

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- April 24th 2010, 10:31 PMapple2009primitive root of unity
Let x=e^(2∏/13i), a primitive 13th root of unity.

Find a subfield K of Q(X) with (Q(x):K)=3.

Find a subfield L of Q(X) with (Q(x):L)=4. - April 25th 2010, 02:04 AMaliceinwonderland
Let be the primitive 13th roots of unity. We see that , where the generator of this cyclic group is .

You need to find the subgroup of the order 3 and order 4 for the above group and correspond them to the subfields of .

The subgroup of order 3 for is generated by .

Thus , where .

You can find the L exactly in the same way.