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May 20, 2013 at 2:11 comment added Will Sawin Clearly the torsion subgroup remains finite, because adding infinitely many new roots of unity requires an infinite degree field extension. So the main question is whether the torsion-free quotient is free.
May 20, 2013 at 0:00 history asked Josué Tonelli-Cueto CC BY-SA 3.0