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Author Archives: Peter Cameron
An apology
What would life be like if I could remember all the things I ever knew? Yesterday I was led to something I posted here twelve years ago. This was based on a talk to the London Algebra Colloquium by Mark … Continue reading
Posted in doing mathematics
Tagged conjugacy supercommuting graph, Jordan's theorem, Mark Wildon
4 Comments
A week in Florida
The week before last I was at the Deerfield Beach Resort in Florida, about halfway between Miami and Donald Trump’s place. My children could not believe it when I told them (I am not very good at holidays). Of course … Continue reading
Cambridge
This is in a sense a followup to my earlier post here, describing how the 6month programme at the Isaac Newton Institute had come to a premature end because of the covid pandemic. The time I spent in Cambridge then … Continue reading
The enhanced power graph is weakly perfect
Earlier this year, I posed a combinatorial problem, a solution to which would imply that, for any finite group G, the enhanced power graph of G is weakly perfect, that is, has clique number equal to chromatic number. Recall that … Continue reading
Posted in doing mathematics
Tagged chromatic number, clique number, enhanced power graph, Euler's totient
19 Comments
More on the 3p paper
I wrote here about Peter Neumann’s paper on primitive permutation groups of degree 3p, where p is a prime number. Well, summer is almost over, but my undergraduate research intern Marina AnagnostopoulouMerkouri and I have done our work and produced … Continue reading
Student meetings
Lots of things have happened and not been noted, sorry. I will try to catch up a bit over the next few weeks. In the past few weeks I have spoken at two studentorganised conferences. First, in July, was the … Continue reading
BCC29 at Lancaster
Last week we celebrated the 29th British Combinatorial Conference in Lancaster, face to face. (As a side observation, this was by far the largest social gathering I have been at since the start of the pandemic; I found it both … Continue reading
Why I’d like to see this solved
I am aware that quite a number of people have been captivated by the problem I posed. So here is the motivation for it, with some additional remarks and commennts. First, to repeat the problem: Problem: Let n be a … Continue reading
Posted in doing mathematics
Tagged chromatic number, enhanced power graph, GruenbergKegel graph
3 Comments
A request
In 1956, Helmut Wielandt proved that a primitive permutation group whose degree is twice a prime p is doubly transitive, unless p has the form 2a2+2a+1, in which case the group has rank 3, and its subdegrees are a(2a+1) and … Continue reading
I’d like to see this solved
Here is a problem that I would really like to see solved. I have spent quite a bit of time on it myself, and have suggested it to a few other people, but it still resists all attacks, though it … Continue reading
Posted in doing mathematics, open problems
9 Comments