Changes

The homology groups with coefficients in an abelian group $M$ are given as follows:
$H_q(\mathbb{Z}/p\mathbb{Z} \oplus \mathbb{Z}/p\mathbb{Z};M) = \left\lbrace\begin{array}{rl} (M/pM)^{(q+3)/2} \oplus (\operatorname{Ann}_M(p))^{(q-1)/2}, & \qquad q = 1,3,5,\dots\\ (M/pM)^{q/2} \oplus (\operatorname{Ann}_M(p))^{(q+2)/2}, & \qquad q = 2,4,6,\dots \\ M, & \qquad q = 0 \\\end{array}\right.$
Here, $M/pM$ is the quotient of $M$ by $pM = \{ px \mid x \in M \}$ and $\operatorname{Ann}_M(p) = \{ x \in M \mid px = 0 \}$.