10.54 (1986)

(R. Göbel). For a cardinal number $\mu$, let
$$\mathbb{Z}^{<\mu} = \{f \in \mathbb{Z}^\mu \mid \lvert\operatorname{supp} (f)\rvert < \mu\} \quad \text{and} \quad G_\mu = \mathbb{Z}^\mu / \mathbb{Z}^{<\mu}.$$ $\qquad$ a) Find a non-zero direct summand $D$ of $G_{\omega_1}$ such that $D \ncong G_{\omega_1}$.
$\qquad$ b) Investigate the structure of $G_\mu$ (the structure of $G_{\omega_0}$ is well known).