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# Author Archives: Peter Cameron

## Combinatorial Theory

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

## The Fitting subgroup

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 Fitting subgroup, Frattini argument, nilpotence, Sylow's theorem
3 Comments

## On the Frattini subgroup

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 Frattini subgroup, G. A. Miller, writing mathematics
4 Comments

## Surprising fun fact

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

## Integrals of groups revisited

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

Posted in doing mathematics, exposition
Tagged Carlo Casolo, derived subgroup, Sofos Efthymios
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## Moonlighting

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

Posted in events
Tagged axial algebras, big Ramsey degrees, Deza graphs, dual Seidel switching, EPPA, Greenberg's theorem, Hardy fields, Helmut Wielandt, indivisibility, integral graphs, Latin cubes, Markov numnbers, Miguel Couciero, Natalia Maslova, profile, strongly 2-closed groups, surreal numbers, Thompson groups, twin-width
6 Comments

## A problem

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

## Communication

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

## Puzzle solution

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

Posted in exposition
Tagged countable random graph, Henson graphs, hereditarily finite set theory, Rado graph
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