It is well known that $n=6$ is the only number greater than two in which there is no Graeco-Latin square of order $n$. It is also well known that $n=6$ is the only number greater than two in which there is an outer automorphism of the symmetric group $S_n$. Is there a connection between these two interesting facts or is it just a coincidence?
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asked May 1, 2019 at 1:39
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2$\begingroup$ Why greater than 2? There is also no outer automorphism of $\mathrm S_0 \cong \mathrm S_1$ or $\mathrm S_2$. $\endgroup$– LSpiceCommented May 8, 2019 at 1:44
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$\begingroup$ I just wanted to keep things nontrivial. $\endgroup$– Craig FeinsteinCommented May 8, 2019 at 16:40
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