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Over the integers
The even and odd cases can be combined giving the following alternative description:
<math>H_q(\mathbb{Z}/p\mathbb{Z} \oplus \mathbb{Z}/p\mathbb{Z};\mathbb{Z}) = \left\lbrace \begin{array}{rl} (\mathbb{Z}/p\mathbb{Z})^{q/2 + 3(1 - (-1)^q)/4} , & q > 0 \\ \mathbb{Z}, & \qquad q = 0 \\\end{array}\right.</math>
The first few homology groups are given below:
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