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Is it possible to construct series of groups $G_i, |G_i|\mapsto \infty$ and functions $f_i:G_i\mapsto$ {$ 1,0,-1$} such that $f_i(1)=0$, $f_i(g) \in ${$-1,1$} for $g\neq 1$ such that dimension of $C[G_i]*f_i$ is small (i.e. $\dim C[G_i]*f_i\leq O(|G_i|^{\varepsilon })$ for every $\varepsilon>0$).

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  • $\begingroup$ What do you mean by $C[G_i] \ast f_i$? $\endgroup$
    – Faisal
    Apr 3, 2011 at 22:22
  • $\begingroup$ $C[G_i]*f_i$ is a left ideal of the group algebra $\endgroup$ Apr 4, 2011 at 0:40

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