Problem Contest – Problem of the Week -September 30, 2003
Exploring automorphisms: An automorphism, g, of a field F (e.g., the reals or the rationals) is a one-to-one mapping of F onto itself such that g(a+b) = g(a) + g(b) and g(ab) = g(a)g(b) for all a,b in F. In words, this means that g "preserves" addition and it "preserves" multiplication in the field. If F is the field of rational numbers, how many different automorphisms of F are there?
Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, October 7. Or leave them in the Warner mailroom.
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