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,…
R. Schaeffer, B. Miranda, and S. Koyejo. Proceedings of the 37th International Conference on Neural Information Processing Systems, page 55565--55581. Red Hook, NY, USA, Curran Associates Inc., (Dec 10, 2023)