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Apr 23, 2010 at 13:26 comment added Torsten Ekedahl @Robin: Right I saw potential problems only because for some strange reason I had confused what was subgroup of what.
Apr 23, 2010 at 12:29 comment added Robin Chapman The class number is irrelevant. If $K$ is a number field, then $K^*$ is isomorphic to the direct product of a finite cyclic group (whose order is the number of roots of unity in $K$) with a free abelian group of infinite countale rank.
Apr 23, 2010 at 11:04 comment added Torsten Ekedahl You are right, what I wrote is true but invalidates the following arguments. Corrected.
Apr 23, 2010 at 11:02 history edited Torsten Ekedahl CC BY-SA 2.5
Put "countable" in the right position.
Apr 23, 2010 at 10:42 comment added naf I suppose you meant a free abelian group with a countably infinite basis...
Apr 23, 2010 at 10:00 history answered Torsten Ekedahl CC BY-SA 2.5