# Hatcher 2.1.31

Hatcher, Algebraic Topology, Chapter 2, Section 1

31. Using the notation of the five-lemma, give an example where the maps $\alpha$, $\beta$, $\delta$, $\varepsilon$ are zero but $\gamma$ is nonzero. This can be done with short exact sequences in which all the groups are either $\mathbb{Z}$ or 0.
Proof.

$\square$