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Thread: Number of group homomorphisms

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    Number of group homomorphisms

    My solution to this problem, although it can be generalized to any finite abelian group $\displaystyle G$, is not straightforward. See if you can find a simple solution:

    Let $\displaystyle p$ be a prime number. Let $\displaystyle G_1$ and $\displaystyle G_2$ be cyclic groups of orders $\displaystyle p$ and $\displaystyle p^2$ respectively. Let $\displaystyle G=G_1 \times G_2.$ Find the number of group homomorphisms $\displaystyle f: G \longrightarrow G.$
    Last edited by NonCommAlg; Jun 8th 2010 at 11:46 AM.
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