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# Author Archives: Peter Cameron

## Graphs on groups, 12

One thing I have learned from the project is that the most interesting question about graphs defined on groups is this: given two types of graph defined on a group G, what is the class of groups for which the … Continue reading

Posted in doing mathematics, exposition
Tagged enhanced power graph, independence graph, power graph, rank, supersoluble group
1 Comment

## Graphs on groups, 11

A brief interlude to describe another recent preprint, and as in the preceding post I will concentrate on one result in the paper. I don’t know why it happens, but in this project one of the most interesting graph parameters … Continue reading

Posted in doing mathematics, exposition
Tagged clique number, nilpotent group, solubility graph, souble group
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## Graphs on groups, 10

The lesson of this post and the next in the series is that the most interesting questions (to me, anyway) are not about the girth of the deep commuting graph but instead about the classes of groups G defined by … Continue reading

Posted in doing mathematics, exposition
Tagged 2-Engel group, commuting graph, conjugacy, Dedekind group, enhanced power graph, power graph
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## Happy new year

Happy new year, everyone. Although I can’t see the end of the Covid tunnel yet, I do hope that for all of us the new year brings better times. One big change for me in the coming year is that, … Continue reading

## Two pointers

As you know, this is where I take out my frustrations by having a good grumble about life, the universe, and everything. Yesterday, in a meeting, we learned of two developments coming to the academic world. In neither case is … Continue reading

## Graphs on groups, 9

We continue to make progress with the graphs on groups project, but this post attempts to step back and look at the whole thing. What use is all this? Once, after I talked at a departmental colloquium at the University … Continue reading

Posted in doing mathematics, exposition, open problems
Tagged graph theory, group theory, number theory, open problems
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## COP26

If I could send a message to the world leaders who will soon assemble in Glasgow, it would be, in the words of a St Andrews honorary graduate: What’ll you do now, my blue-eyed son?What’ll you do now, my darling … Continue reading

## Joachim Neubüser

Another sad loss, with the death of Joachim Neubüser this week. He was the driving force behind the creation of the computer algebra system GAP. Even though I worked with John Cannon, the creator of the rival system Magma, I … Continue reading

## Clive Sinclair

Yesterday I read the news that Clive Sinclair has died. This brought back memories of my first encounter with personal computers nearly 40 years ago. At the time I had a demanding job and three small children, and I was … Continue reading

Posted in doing mathematics, history, open problems
Tagged Neil Calkin, sum-free sets, ZX Spectrum
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## Graphs on groups, 8

The dark clouds seem to have lifted a bit. Perhaps now, that the last rush of conferences for a while is over, life can return to something like normality … For me the most significant event was the last in … Continue reading

Posted in doing mathematics, events, open problems
Tagged graphs and groups, matching number, power graph
3 Comments