Is the Galois group of F=Q(sqrt2,3i) the maps {id, tau , sigma, gamma}, where
(1) id is the identity
(2) tau maps sqrt2 to -sqrt2 and leave 3i alone
(3) sigma leaves sqrt2 alone and maps 3i to -3i
(4) gamma maps sqrt2 to -sqrt2 and 3i to -3i ?
If so, the what are the fixed fields of the...