Dense Bogolyubov-Ruzsa lemma
= Dense Bogolyubov-Ruzsa lemma
{c}
For every $\alpha>0$, if $A$ has density at least $\alpha$ in a cyclic group of prime order, then $2A-2A$ contains a proper <generalized arithmetic progression> of rank $O_\alpha(1)$ and size $\Omega_\alpha(|G|)$.