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Jan 25, 2010 at 13:10 comment added Gerald Edgar An my thought was: direct sum of copies of Q. I.e., the dimension of the vector space. For every cardinal there is a vector space with that dimension, and spaces with different dimension (over Q) are not isomorphic as groups.
Jan 25, 2010 at 9:09 history answered Gerhard Paseman CC BY-SA 2.5