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# Category Archives: symmetric group

## The symmetric group, 3

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 … Continue reading

Posted in exposition, history, symmetric group
24 Comments

## The symmetric group, 2

To continue my series on the symmetric group, I want to consider the question: What is the role of the symmetric group in mathematics? First, a diversion. What is the role of graphs in mathematics? I would say that graphs … Continue reading

Posted in exposition, symmetric group
6 Comments

## The symmetric group, 1

This is the first of a short series of posts which will try to look at the symmetric group in slightly fresh ways. It is in part a fraternal greeting to my friends on SymOmega, who named their blog after … Continue reading

Posted in books, exposition, numbers, symmetric group
9 Comments