On the structure of \(K_2(\mathbb{Z}[C_2 \times C_2])\) (Q343576)

Let \(C_2\) be the group of order two. It is shown that \(K_2(\mathbb Z [C_2\times C_2])\) is isomorphic to \((\mathbb Z/2)^6\). An explicit basis is given in terms of Dennis-Stein symbols. The computation requires numerous results from the literature. As an application, it is found that \(Wh_2(C_2\times C_2)\) is isomorphic to \((\mathbb Z/2)^2\).