What does this notation mean? Perhaps related to abelian group and module.

Question

I found this in a paper, but I don't it's meaning. Where H is an abelian group, what does $ \bigwedge ^{2} H $ mean? If H is a dual vector space, perhaps it is wedge product. But I don't know when it comes to an Abel group.

Answer 1

You can apply the same definition $\bigwedge^2H=(H\otimes H)/\langle \,h\otimes h\mid h\in H\, \rangle $ with $\otimes$ meaning the tensor product as $\mathbb Z$-modules