### Top Posts

### Recent comments

- Prabir Bhattacharya on John McKay
- Peter Cameron on John McKay
- ENOCH SULEIMAN on John McKay
- ENOCH SULEIMAN on Peter Neumann memorial meeting
- Jon Awbrey on Taylor series

### Blogroll

- Astronomy Picture of the Day
- Azimuth
- British Combinatorial Committee
- Comfortably numbered
- Diamond Geezer
- Exploring East London
- From hill to sea
- Gödel's lost letter and P=NP
- Gil Kalai
- Jane's London
- Jon Awbrey
- Kourovka Notebook
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Ratio bound
- Robert A. Wilson's blog
- Since it is not …
- Spitalfields life
- Sylvy's mathsy blog
- SymOmega
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The ICA
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- XKCD

### Find me on the web

### Cameron Counts: RSS feeds

### Meta

# Category Archives: symmetric group

## Au revoir, GRA

Today (Wednesday 18 March) the Groups, Representations and Applicatons programme at the Isaac Newton Institute came to a premature end. There are still some hopes that it can be revived later, but at the moment the only certainty is that … Continue reading

Posted in doing mathematics, symmetric group
Leave a comment

## Chains of semigroups

I have written here about the lovely formula for the length of the longest chain of subgroups in the symmetric group Sn: take n, increase it by 50% (rounding up if necessary), subtract the number of ones in the base … Continue reading

## Remoteness

After the last bit of bureaucratic nonsense, what a relief to turn to mathematics again. Maximilien Gadouleau and I have just submitted a paper about a concept for finite metric spaces somewhat related to domination, which we call remoteness. It … Continue reading

## The symmetric group, 12

This instalment is about the maximal subgroups of the symmetric group, and the O’Nan–Scott Theorem. There are two versions of this theorem, one of which is sometimes called the Aschbacher–O’Nan–Scott Theorem. One is about maximal subgroups of the symmetric group … Continue reading

Posted in exposition, symmetric group
Tagged maximal subgroups, O'Nan-Scott theorem, permutation group, symmetric group
6 Comments

## The symmetric group, 11

I am going to talk about a celebrated theorem of John Dixon and some of its variants; this is on my mind at the moment, for reasons I will explain at the end. Dixon’s theorem is easily stated. Two random … Continue reading

Posted in exposition, symmetric group, synchronization
Tagged Baire category, Dixon's theorem, symmetric group
4 Comments

## The symmetric group, 9

There are many different ways to regard a finite symmetric group as a metric space. These have been used for various purposes. Here I would like to say something about them. One application of such metrics is in non-parametric statistics. … Continue reading

Posted in exposition, mathematics, symmetric group
2 Comments

## The symmetric group, 6

I quote here the review on MathSciNet for a paper which appeared in a conference proceedings in 1970. (This review, of course, was published in Mathematical Reviews, and now has been put on the website.) I have made one correction, … Continue reading

## The symmetric group, 5

Time to say a bit about the combinatorics of the symmetric group. Certainly not a complete survey of a vast topic, which would be quite impossible; I will touch on just a few things. Loosely speaking, the subject divides into … Continue reading

Posted in exposition, open problems, symmetric group
4 Comments

## The symmetric group, 4

One of my views on teaching abstract algebra, with which my colleagues don’t all agree by any means, is that it is better to do rings before groups. The view for putting groups first is that they have just a … Continue reading

Posted in exposition, symmetric group
7 Comments