The tensor product of the finitely generated abelian group G with a rational number is zero if and only if G is finite. is it true for any finite group? For example, we take the tensor product of the symmetric group with a rational number. This group is zero or not.
2026-03-25 17:21:40.1774459300
Tensor product of finite group with group of rational number.
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If $A$ is an Abelian group (written additively), then $A\otimes\Bbb Q=0$ iff $A$ is torsion. Of course, all finite groups are torsion. But if $A$ is non-Abelian, then I'm not sure that $A\otimes \Bbb Q$ makes sense.