Comments on: The symmetric group, 1

By: Ralph

Ralph — Fri, 15 Jun 2012 16:08:08 +0000

All conjugacy classes of subgroups… isn’t that the same as all integer partitions of subgroups?

By: Peter Cameron

Peter Cameron — Thu, 14 Jun 2012 15:21:27 +0000

As I said, Alexander Hulpke has the best results about small values, and he is also extremely helpful. You might start with his stuff. I might say more about this later – but now, just back from giving the course on Laplacian eigenvalues, I am tired!

By: Ralph

Ralph — Wed, 13 Jun 2012 21:46:23 +0000

I found the Geoffrey of Monmouth Lear and am reading it now.

I am extremely interested to learn more about your additional kinds of ordinal numbers. The concept gives me several ideas, particularly about rational numbers.

Is there a web site or text to which I might refer to understand why the subgroups and their conjugacy classes are so difficult to compute? It seems that S3 is a subgroup of S4, and so forth — so I can see that the subgroups might pile up — but faster than n! itself? Seriously?

By: Peter Cameron

Peter Cameron — Wed, 13 Jun 2012 08:39:19 +0000

You have the advantage over me there. I know Geoffrey of Monmouth’s Lear, but never managed to get right through Shakespeare’s. (In Geoffrey the story has a happy ending.)

I will probably get round to saying something about conjugacy sometime…

By: Ralph Dratman

Ralph Dratman — Tue, 12 Jun 2012 17:06:31 +0000

I want to say I feel fortunate to know about this blog. It is like attending a tutorial class. I am slow at piecing things together in my mind, and it seems that I often see things in a peculiar way. Perhaps that is why I like your approach, which I see as naive in the best sense, uncluttered by prejudice, and open to new discussion of old topics without limitation.

As for the conjugacy classes, I intend to keep trying to understand. I feel sure I will get it eventually.

By: Ralph Dratman

Ralph Dratman — Tue, 12 Jun 2012 16:15:07 +0000

“And who can remember the difference between King Lear’s daughters Goneril and Regan?”

I am almost certain it was Regan who started plucking hairs out of Lear’s beard, for no obvious reason, when he was helpless. It is an act of savagery for which I cannot personally forgive her.

Between Rosencrantz and Guildenstern, however, I do not think there is any real difference. Gertrude even has to say their names first in one order, then in the other, when pleading with them to probe Hamlet’s thoughts — probably because she could never remember which was which.

By: On the symmetric group « Peter Cameron's Blog

On the symmetric group « Peter Cameron's Blog — Thu, 21 Oct 2010 15:20:15 +0000

[...] of places, including the SymOmega blog and Ron Adin‘s course on the symmetric group, refer to my first post in a short series on this [...]

By: The symmetric group, 2 « Peter Cameron's Blog

The symmetric group, 2 « Peter Cameron's Blog — Wed, 05 May 2010 09:00:06 +0000

[...] symmetric group, 2 By Peter Cameron To continue my series on the symmetric group, I want to consider the question: What is the role of the symmetric group in [...]