Corners over quasirandom groups

Let $G$ be a finite $D$-quasirandom group and $A\subset G^k$ a $\delta$-dense subset. Then the density of the set of side lengths $g$ of corners $$\{(a_1,\dots ,a_k),(g{a}_1,a_2,\dots ,a_k),\dots ,(g{a}_1,\dots ,g{a}_k)\}\subset A$$ converges to $1$ as $D\to \mathrm{\infty }$.