Tag Archives: CFSG

A small problem

Posted on 26/07/2021 by Peter Cameron

In connection with the research discussion about graphs and groups, I began to wonder which finite groups have the property that any two elements of the same order are conjugate. I thought about this, and got a certain distance, and … Continue reading →

Posted in open problems | Tagged , , | 1 Comment

Prospects in Mathematics, 2

Posted on 24/12/2016 by Peter Cameron

I didn’t say anything about my own talk at the Prospects in Mathematics meeting. But soon afterwards I was re-reading Lee Smolin’s 2006 book The Trouble with Physics, and it resonated with some of the things I said. My topic … Continue reading →

Posted in doing mathematics, events | Tagged , , , | 7 Comments

Commuting graph, 2

Posted on 25/02/2013 by Peter Cameron

Last week Chris Parker gave a very interesting talk in the London Algebra Colloquium on this topic. It is an excellent example of a curious phenomenon. If you look for your keys under the lamppost, then in a Borgesian way … Continue reading →

Posted in exposition | Tagged , , , | Leave a comment

Finding derangements without CFSG

Posted on 18/01/2013 by Peter Cameron

Nearly two years ago, I posed the problem of finding an “elementary” deterministic polynomial-time algorithm for finding a fixed-point-free element (or derangement) in a transitive permutation group. The background is that there are so many fpf elements (at least a … Continue reading →

Posted in exposition | Tagged , , | Leave a comment

Finite simple groups

Posted on 15/01/2013 by Peter Cameron

The blog Gödel’s Last Letter and P=NP is always worth reading. The two bloggers, RJ Lipton and KW Regan, are computer scientists, but they have interesting things to say about developments in mathematics, and other areas too. For example, last year they … Continue reading →

Posted in exposition | Tagged , , , , , | 2 Comments

A permutation group challenge, 3

Posted on 02/01/2013 by Peter Cameron

“Then I will do it myself”, said the little red hen. And she did. Since nobody took up the challenge, I had to do it myself. Let λ be a partition of n. We say that a permutation group G … Continue reading →

Posted in open problems | Tagged , , | Leave a comment

A permutation group challenge

Posted on 19/12/2012 by Peter Cameron

Long ago, in the distant past before the Classification of Finite Simple Groups, Peter Neumann, Jan Saxl and I investigated the class of permutation groups acting on sets of even cardinality n = 2k, with the following interchange property: Any subset of … Continue reading →

Posted in exposition, open problems | Tagged , , , | 1 Comment

35ACCMCC at Monash

Posted on 10/12/2011 by Peter Cameron

I’ve just spent a week at the 35th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing at Monash University in Clayton, a suburb of Melbourne. The conference happened to coincide with a research visit to Monash, about which I will … Continue reading →

Posted in events | Tagged , , , , , | 11 Comments