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Find $a$ satisfying $x \cup_1 y = \delta a$ when $x,y \in Z^2(G,\mathbb{Z}_2)$

Let $G$ be a finite group. Let $x,y \in Z^2(G,\mathbb{Z}_2)$ be 2-cocycles. Find $a \in C^2(G,\mathbb{Z}_2)$ such that \begin{align} x \cup_1 y = \delta a. \end{align} Is there a general solution? Is …
A_Physicist.'s user avatar