MATH 422 Midterm: MATH 422 2016 Winter Test 1
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Id number: the test consists of six questions on eight pages, no calculators or notes or books allowed, if you need more space for a problem, continue on the back of the page or on a separate paper. But label clearly that your answer continues somewhere else: you can use (without proof) any statement we"ve proven in class or on the homework. If you"re unsure whether something counts, ask me. Eld of an irreducible polynomial of degree 24. Find a galois extension k/q with gal(k/q) = z3 z3 z3 as a sub eld of a cyclotomic. Eld q( n), by coming up with a speci c integer n and explaining how you can construct a subgroup. H gal(q( n)/q) such that the xed eld k = q( n)h works. It turns out that one can get a galois extension m/q with gal(m/q) = q8 by setting.
