Inspired by the construction of the non-mesurable Vitali set I thought about the group $\mathbb{R}/\mathbb{Q}$ (the additive group of the real numbers modulo the rationals). There must be some literature for this, but I haven't found any and it is hard to google. Does anyone know where to find results about this group?
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4Cf: http://math.stackexchange.com/questions/355852/what-is-known-about-the-quotient-group-mathbbr-mathbbq – Daniel Pietrobon Nov 17 '13 at 12:36