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Questions about the branch of algebra that deals with groups.

32 votes
3 answers
3k views

morphism from a compact group to Z ?

I wonder if it there exists a topological compact group $G$ (by compact, I mean Hausdorff and quasi-compact) and a non-zero group morphism $\phi : G \to \mathbb{Z}$ (without assuming any topological …
Florent MARTIN's user avatar
1 vote
3 answers
1k views

group scheme neither affine, nor an abelian variety

Does there exist a group scheme of finite type over a field $k$ , which is neither affine, nor an abelian variety?
Florent MARTIN's user avatar