(3.) Consider Q(n)/Q where n = exp(27i/5). Show this is a quartic extension and find its...

 

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(3.) Consider Q(n)/Q where n = exp(27i/5). Show this is a quartic extension and find its Galois group and intermediate field. Draw the lattice diagrams both for Gal(Q(n)/Q) and Q(n)/Q. Comment on the fixed field correspondence. (3.) Consider Q(n)/Q where n = exp(27i/5). Show this is a quartic extension and find its Galois group and intermediate field. Draw the lattice diagrams both for Gal(Q(n)/Q) and Q(n)/Q. Comment on the fixed field correspondence.

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