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Dec 20, 2014 at 16:58 comment added David E Speyer In the positive direction, I recently encountered a result of Hoehnke and Johnson, arxiv.org/abs/math/9210219 : A group is determined by the collection of functions $G^k \to \mathbb{C}$ for $k=1$, $2$ and $3$ given by $g \mapsto \chi(g)$, $(g,h) \mapsto \chi(g)\chi(h)- \chi(gh)$ and $(f,g,h) \mapsto \chi(f) \chi(g) \chi(h) - \chi(fg) \chi(h) - \chi(gh) \chi(f) - \chi(h) \chi(fg) + \chi(fgh) + \chi(fhg)$ for all characters $\chi$.
Jan 11, 2010 at 16:45 history edited David E Speyer CC BY-SA 2.5
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Jan 10, 2010 at 22:10 comment added Steven Sam Here's a link to the paper: dx.doi.org/10.1016/0021-8693(64)90002-X
Jan 10, 2010 at 21:44 comment added David E Speyer Nice! I don't think I would have found that. I've added the link for you.
Jan 10, 2010 at 21:43 history edited David E Speyer CC BY-SA 2.5
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Jan 10, 2010 at 20:23 history edited Mariano Suárez-Álvarez CC BY-SA 2.5
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Jan 10, 2010 at 20:18 history answered Mariano Suárez-Álvarez CC BY-SA 2.5