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# Author Archives: Peter Cameron

## A small problem

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

## Bad times

Apologies for this. If you don’t like reading personal news, especially bad news, don’t persist. I am writing it down in the hope of putting it behind me. Back in early April, Rosemary had a very bad fall on the … Continue reading

Posted in Uncategorized
11 Comments

## A little problem

In connection with the power graphs of unitary groups, I came across the following little number-theoretic conundrum. Can anyone solve it? Let q be an odd power of 2 (bigger than 2). Show that (q2−q+1)/3 is not a prime power … Continue reading

## A new constant?

This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading

Posted in doing mathematics, open problems
Tagged clique number, Euler's function, power graph
8 Comments

## Graphs on groups, 7

Nothing much to report, just a few connections. My long paper has appeared on-line ahead of publication in the International Journal of Group Theory. You can get a copy here (click on PDF). Next week, on Wednesday 12 May at … Continue reading

## Graphs on groups, 6

The Groups and Graphs seminar has been running well. I find that I feel close to many people in the seminar even though most likely we have not met face to face. So I feel concerned about the Covid wave … Continue reading

## EDI

We hear a lot about equality, diversity and inclusion now. Perhaps it would be good to remind ourselves of the formal definition. A and B are equal if, for all x, we have (x∈A) ↔ (x∈B). A and B are diverse if … Continue reading

## Graphs on groups, 5

I gave two lectures on this stuff to a new research seminar on Groups and Graphs, run by Vijayakumar Ambat in Kochi, Kerala. The first was an introduction to the hierarchy, the second was about cographs and twin reduction, why … Continue reading

Posted in events, exposition, open problems
Tagged cograph, commuting graph, nilpotent group, perfect graph, power graph
2 Comments

## Hoffman, Lovász and Haemers

At the weekend I attended remotely a memorial session for Alan Hoffman, organised by Bill Pulleyblank. I found it informative, as well as moving. Hoffman is well-known in the algebraic graph theory community for a number of remarkable achievements, including … Continue reading

Posted in events
Tagged Alan Hoffman, algebraic graph theory, eigenvalues, Laszlo Lovasz, optimization, WIllem Haemers
1 Comment

## Three passages

[Dmitri] Egorov [founder of the Moscow School of Mathematics] was a very reserved and modest man, so much so that it would be easy to believe that he lived only for mathematics. […] His publications do not reveal any evidence … Continue reading

Posted in Uncategorized
5 Comments