# Set of Rotations is Subgroup of Symmetry Group

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## Theorem

Let $G$ be a symmetry group.

Let $H$ be the subset of $G$ consisting of the rotations in $G$ about a given axis.

Then $H$ is a subgroup of $G$.

## Proof

This theorem requires a proof.In particular: Needs a more formal definition of rotation. Surprised this hasn't already been covered properly.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1996: John F. Humphreys:
*A Course in Group Theory*... (previous) ... (next): Chapter $4$: Subgroups: Example $4.5$