Corpus ID: 3562799

THE EXCEPTIONAL SYMMETRY

@article{McCammond2014THEES,
  title={THE EXCEPTIONAL SYMMETRY},
  author={Jon McCammond},
  journal={arXiv: Group Theory},
  year={2014}
}
This note gives an elementary proof that the symmetric groups possess only one exceptional symmetry. I am referring to the fact that the outer automorphism group of the symmetric group Symn is trivial unless n = 6 and the outer automorphism group of Sym6 has a unique nontrivial element. When we study symmetric groups, we often invoke their natural faithful representation as permutations of a set without a second thought, but to what extent is this representation intrinsic to the structure of… Expand

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References

SHOWING 1-8 OF 8 REFERENCES
Sphere Packings, Lattices and Groups
  • J. Conway, N. Sloane
  • Mathematics, Computer Science
  • Grundlehren der mathematischen Wissenschaften
  • 1988
Designs, graphs, codes, and their links
The Beauty Of Geometry
The beauty of geometry, Dover Publications, Inc
  • Mineola, NY,
  • 1999