Timeline for Is there a non-degenerate quadratic form on every finite abelian group?
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| Oct 16, 2020 at 19:48 | comment | added | Qiaochu Yuan | The generalization I guess is to observe that when you pass from a bilinear form $B$ to a quadratic form $Q$ to a bilinear form again you end up with $2B$, so for $B$ to induce a quadratic form it suffices for $2B$ to be a bilinear form, not $B$; so you can take pointwise square roots of a bilinear form (my apologies for switching back to thinking multiplicatively here) and the result will still induce a genuine quadratic form. Of course these will only be non-unique if there's $2$-torsion. | |
| Oct 14, 2020 at 23:36 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |