# Tag Archives: permutation group

## A problelm

Given a finite permutation group G on a set X, the permutation character π of G is the function on G mapping an element g to its number of fixed points in X. This is a character of G, the … Continue reading

Posted in open problems | | 2 Comments

## A problem

Since I have been saying rather a lot about association schemes and coherent configurations lately, I thought I would mention an open problem. This is probably one for the experts, and I guess it has been ignored because of the … Continue reading

Posted in open problems | | 8 Comments

## Imprimitive permutations in primitive groups

Asymptotics of permutation counts is a subject with a long history. The result that the proportion of permutations which are derangements (that is, have no fixed points) is very close to 1/e is one of the oldest results in enumerative … Continue reading

## Three versus four

The title is homage to the Gödel’s Last Letter and P=NP blog, which a week ago had a post entitled Two versus three. At the problem session at the Banff meeting last night, Dugald Macpherson and Andras Pongracz posed various … Continue reading

## Computational group theory, 1

Computational group theory is the art or science of using a computer to learn something about a group. I was introduced to it by John Cannon in the early 1980s. It seems like a black art to many mathematicians (myself … Continue reading

Posted in exposition | | 1 Comment

## Groups, lattices and bases

About ten years ago I wrote a six-page paper, which I didn’t succeed in getting any journal editor to publish. I will say a bit about its contents below, but you can read it now: I have posted it on … Continue reading

Posted in exposition | | 3 Comments

## 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 | | 6 Comments