I've been reading some notes on group cohomology and there are repeated mentions of the following:
For a group $G$, $H^1(G,\mathbb Q/\mathbb Z)=Hom(G,\mathbb Q/\mathbb Z)$. It may be very easy, but can anyone please point out to me why that is true? I also noted that the notes deals with finite groups $G$, but I think this may be true for all groups. The interpretation of first cohomology group I'm considering is the one discusses here: Interpretations of the first cohomology group. But I'm still missing the point why this is true.