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I solved other problems, except (d): if $\beta$ is injective, $\alpha$ and $\gamma$ are surjective, then $\gamma$ is injective.

Unlike others, I don't know where to start.

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    This is a typo in the book: the first $\gamma$ should be a $\varphi$. See [the errata](http://www.cems.uvm.edu/~foote/errata_3rd_edition.pdf) on Foote's webpage.2012-03-07
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    Yep, a typo, you can easily find a counterexample to the statement as it is written.2012-03-07
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    Thanks, guys! I lost a few hours thinking over this.2012-03-07
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    @Dylan Making your comment an answer, perhaps with a counter example, will resolve this question. Please consider this. Regards,2012-03-14

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