No account of the symmetric group can be complete without mentioning the remarkable fact that the symmetric group of degree n (finite or infinite) has an outer automorphism if and only if n=6. Here are the definitions. An automorphism of a group G is a permutation p of the group which preserves products, that is,…
S. Oviatt, A. Cohen, and N. Weibel. Proceedings of the 15th ACM on International Conference on Multimodal Interaction, page 563--568. New York, NY, USA, ACM, (2013)Workshop.