Let \(G\) be a finite Abelian group with \(\#G=p\). For \(A,B\subset G\) let \(m(x,A,B)=\#\{(a,b): a+b=x,\;a\in A,\;b\in B\}\). For \(E\subset G\) let \(E'\) denote its complement. The authors prove the following results: \[ \begin{multlined}\sum_{c\in G} |m(x,E,E)+m(x,E',E')-m(x,E,E')-m(x,E',E)|^2= \\ \sum_{c\in G} |m(x,E,-E)+m(x,E',-E')-m(x,E,-E')-m(x,E',-E)|^2\end{multlined}\tag{i) (Cohesion equation} \] \[ \min_{E\subset G}\max_{x\in G}|m(x,E,E)+m(x,E',E')-2m(x,E,E')|\geq p^{1/2}\tag{ii} \] If \(\lambda>\frac{1}{2}\) and \(G\) contains no element of order 2, then \[ \min_{E\subset G}\max_{x\in G}|m(x,E,E)+m(x,E',E')-2m(x,E,E')|\geq K.p^{\lambda}.\tag{iii} \] Here \(K\) depends only on \(\lambda\).