Word Count : 155

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We decompose the group (\mathbb{Z}*8 \times \mathbb{Z}*{12} \times \mathbb{Z}*{15}) into its primary components. Writing each modulus as a product of prime powers gives (8=2^3), (12=2^2\cdot 3), and (15=3\cdot 5). Hence the (2)-primary part is (\mathbb{Z}*{2^3}\times \mathbb{Z}_{2^2}), the (3)-primary _________ ________ ______ ______ _______ _____ _____ ____.
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