Category Archives: exposition

a post aimed to teach something

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

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Peter Neumann’s 3p paper

In 1955, Helmut Wielandt published a paper proving the following theorem: Let G be a primitive permutation group of degree 2p, where p is a prime greater than 3, which is not doubly transitive. Then p = 2a2+2a+1 for some positive integer … Continue reading

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An O’Nan-Scott note

My old friend Leonard Soicher is visiting St Andrews this week, having made a better job of retiring than I did. Today he gently took me to task for using the expression “simple diagonal type” for one of the types … Continue reading

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Graphs on groups, 13

There are many results about the universality, or otherwise, of various graphs defined on groups: answers to questions of the form “for which graphs Γ is there a group G such that Γ is isomorphic to an induced subgraph of … Continue reading

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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

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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

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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

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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

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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

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Oligomorphic groups: topology or geometry?

One perhaps unexpected result of the pandemic is that there is a huge volume of really interesting mathematics flying around the internet at the moment, courtesy of Zoom and other platforms. This week I went to a talk by Joy … Continue reading

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