1. Galois Theory has made so much more sense with the example shown in this chapter. Most application of it makes sense. In number 8 of the example, I suppose the goal is to first look at the operation, then find out what's fixed inorder to get the right coefficient, finally grouping the terms to get a single term that can represent the fixed fields? How do I know what form I am expecting ( (1+i)E in the example) , or do I just have to try until I found the element?
2. When the Galois group is not isomorphic to a dihedral group, can I still draw a picture like the one in the book?
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