Category Archives: doing mathematics

how is it done?

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

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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

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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 Anagnostopoulou-Merkouri and I have done our work and produced … Continue reading

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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

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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

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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