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,…
J. Berner, P. Grohs, G. Kutyniok, and P. Petersen. (2021)cite arxiv:2105.04026Comment: This review paper will appear as a book chapter in the book "Theory of Deep Learning" by Cambridge University Press.
J. Berner, P. Grohs, G. Kutyniok, and P. Petersen. (2021)cite arxiv:2105.04026Comment: This review paper will appear as a book chapter in the book "Theory of Deep Learning" by Cambridge University Press.
J. Berner, P. Grohs, G. Kutyniok, and P. Petersen. (2021)cite arxiv:2105.04026Comment: This review paper will appear as a book chapter in the book "Theory of Deep Learning" by Cambridge University Press.