TYI 25: The Automorphism Group of the Symmetric Group

True or False: The group of automorphisms of the symmetric group S_n, n ≥ 3 is S_n itself.


This entry was posted in Algebra and Number Theory, Test your intuition and tagged , . Bookmark the permalink.

7 Responses to TYI 25: The Automorphism Group of the Symmetric Group

  1. James says:

    The answer is hard to believe. It reminds me of the smooth structures on $\mathbb{R}^n$.

  2. ameyerowitz says:

    To have anything else happen would be as unlikely as a perfect number which is also a factorial!

  3. aram says:

    I guess you could say that my intuition was correct almost everywhere. 🙂

  4. Gil Kalai says:

    Dear James, Aaron, and Aram – thanks for the comments!

  5. Paco Santos says:

    Coincidentally (?), two days after this was posted John McCammond uploaded a nice little paper to the arXiv containing the answer.

  6. Nick Read says:

    Interesting answer, which I found in a yellow GTM book that I have in my office.

  7. Gil Kalai says:

    Dear Paco and Nick, thanks for the comments. The question came from a talk at HUJI COMBSEM by Sonia Balagopalan and the answer has a role in the minimal triangulation for the 4-dimensional real projective plane. Hmm I wonder what GTM book it was.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s