# Alternating Groups that are Ambivalent

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## Theorem

Let $n$ be a natural number.

Then the $n$th alternating group $A_n$ is ambivalent if and only if $n \in \set {1, 2, 5, 6, 10, 14}$.

This sequence is A115200 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Proof

This theorem requires a proof.In particular: Seems related to the representation theory of alternating group.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. |