Galois group algebra homework help

Question 1. Examples. For each of the following five fields F and and five groups G, find an irreducible polynomial in F[x] such that the Gal(E/F) ∼= G, where E is the splitting field of f(x) over F. Or if no example exists, state that. In either case, you must justify your answer.

Fields F: C, R, F11, Q, Q(i)
Groups G: Z/2Z, Z/5Z, Z/2Z × Z/2Z, S3, D4.

As usual S3 is the third symmetric group, with 6 elements; and D4 is the fourth dihedral group, with 8 elements.

(It might be clearest to arrange your answers in a 5×5 grid. Although you must supply 25 answers, there are some patterns and connections between the different parts. So by being clever, you can cut down a lot on the work.)

 

Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount!
Use Discount Code "Newclient" for a 15% Discount!

NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.