A criterion for double sliceness

We describe a condition involving noncommutative Alexander modules which ensures that a knot with Alexander module $\mathbb{Z}[t^{\pm 1}]\mathrm{/}(t-2)\oplus \mathbb{Z}[t^{\pm 1}]\mathrm{/}(t^{-1}-2)$ is topologically doubly slice. As an application, we show that a satellite knot $R_{\eta }(K)$ is doubly slice if the pattern $R$ has Alexander module $\mathbb{Z}[t^{\pm 1}]\mathrm{/}(t-2)\oplus \mathbb{Z}[t^{\pm 1}]\mathrm{/}(t^{-1}-2)$ and satisfies this condition, and if the infection curve $\eta \subset S^3\setminus R$ lies in the second derived subgroup ${\pi }_1(S^3\setminus R{)}^{(2)}\mathrm{.}$