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Corrected a typo, fixed Latex
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Johannes Hahn
Johannes Hahn
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Each element in the image of $d_n$ corresponds to an element of order $p^n$ in the homology with integer coefficients. So it suffices to compute the image of $d_1=\beta$ on $H_*(X;Z/p)$$H_*(X;\mathbb{Z}/p)$ to determine the number of summands isomorphic to $Z/p$ in $_*(X;Z)$$H_*(X;\mathbb{Z})$.

Each element in the image of $d_n$ corresponds to an element of order $p^n$ in the homology with integer coefficients. So it suffices to compute the image of $d_1=\beta$ on $H_*(X;Z/p)$ to determine the number of summands isomorphic to $Z/p$ in $_*(X;Z)$.

Each element in the image of $d_n$ corresponds to an element of order $p^n$ in the homology with integer coefficients. So it suffices to compute the image of $d_1=\beta$ on $H_*(X;\mathbb{Z}/p)$ to determine the number of summands isomorphic to $Z/p$ in $H_*(X;\mathbb{Z})$.

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user43326
user43326
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Each element in the image of $d_n$ corresponds to an element of order $p^n$ in the homology with integer coefficients. So it suffices to compute the image of $d_1=\beta$ on $H_*(X;Z/p)$ to determine the number of summands isomorphic to $Z/p$ in $_*(X;Z)$.