# (Un)distorted subgroups in the mapping class group: reference required.

Let $S$ be an orientable surface with negative Euler characteristic. Can somebody provide a reference for the following well-known results:

1. the cyclic subgroup generated by a pseudo-Anosov element in the mapping class $MCG(S)$ is undistorted in the mapping class group.

2. the cyclic subgroup generated by a Dehn twist of the mapping class group is undistorted.

3. $\pi_1(S)$ is exponentially distorted in the mapping class group.

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