Author Archives: Peter Cameron

About Peter Cameron

I count all the things that need to be counted.

Combinatorial Theory

Posted on 15/09/2020

I learned yesterday of a new free and open-access journal, Combinatorial Theory, owned by its editorial board. There is a temporary web page here, on which the editorial board (including some familiar names) is listed. This journal joins a list … Continue reading →

Posted in publishing | Tagged , , | 3 Comments

The Fitting subgroup

Posted on 14/09/2020

I have talked a bit about the Frattini subgroup. Time for its big brother. The definition of the Fitting subgroup F(G) of a finite group G is the unique maximal normal nilpotent subgroup of G. As such, of course, it … Continue reading →

Posted in exposition | Tagged , , , | 3 Comments

Groups and graphs

Posted on 08/09/2020

Two new preprints have appeared on the arXiv (2008.09291 and 2009.02884), about which I would like to say something. One is by Saul Freedman, the other by him and two co-authors (his PhD supervisors). The intersection graph of a group … Continue reading →

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On the Frattini subgroup

Posted on 07/09/2020

I wrote earlier about the Frattini subgroup of a group. It can be defined in either of two ways (as the set of non-generators of a group, the elements which can be dropped from any generating set containing them; or … Continue reading →

Posted in doing mathematics, exposition | Tagged , , | 4 Comments

Surprising fun fact

Posted on 06/09/2020

I have just found a proof of the following. Usual caveat: nobody else has read the proof yet, and I have not carefully checked it. Let G be a finite group. The finite group H will be called an inverse … Continue reading →

Posted in doing mathematics | Tagged , | 2 Comments

Integrals of groups revisited

Posted on 04/09/2020

After my trip to Florence in February, I wrote about the work I did there with Carlo Casolo and Francesco Matucci. After Carlo’s untimely death the following month, we were left with many pages of notes from him about the … Continue reading →

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Moonlighting

Posted on 30/08/2020

In the last week of August, I attended for the first time a virtual conference. This was the 2020 Ural Workshop on Group Theory and Combinatorics, organised by Natalia Maslova at the Ural Federal University in Yekaterinburg and her colleagues. … Continue reading →

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A problem

Posted on 19/08/2020

I seem to have too many balls in the air at the moment. So let me drop one here. Any thoughts very welcome. A k-hypergraph consists of a set X of vertices and a collection of k-element subsets called edges. … Continue reading →

Posted in doing mathematics | Tagged | 4 Comments

Communication

Posted on 18/08/2020

If you have been trying to contact me by email at QMUL recently, please try my St Andrews address instead. Inevitably, I suppose, technology tends to fail in the middle of a pandemic. Both QMUL and St Andrews use Outlook … Continue reading →

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Puzzle solution

Posted on 13/08/2020

Thank you, Honza, spot on. In 1964, Richard Rado published a construction of a universal graph, a countable graph which embeds every finite or countable graph as an induced subgraph. His graph turns out to be an explicit example of … Continue reading →

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