Category Archives: doing mathematics

how is it done?

Graphs on groups, 2

Posted on 27/01/2021 by Peter Cameron

I wrote the long post about this to try to write it out of my system. No luck … I mentioned in that survey that every finite graph is embeddable as induced subgraph in the enhanced power graph, deep commuting … Continue reading →

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Ramanujan+100

Posted on 15/12/2020 by Peter Cameron

I have just spent the last four days in Kochi, Kerala, at the International Conference on Number Theory and Discrete Mathematics, commemorating Srinivasa Ramanujan, the great Indian mathematician, on the 100th anniversary of his far-too-early death. The conference had perhaps … Continue reading →

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Oligomorphic groups: topology or geometry?

Posted on 10/12/2020 by Peter Cameron

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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Graphs defined on groups

Posted on 04/12/2020 by Peter Cameron

Apologies; I have been so busy lately that very little has got written up. Let me try to remedy this with a quick tour through some recent mathematical developments. As some of my posts have hinted, one topic I have … Continue reading →

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A paradox, and where it led

Posted on 19/11/2020 by Peter Cameron

What is the difference between a contradiction and a paradox? A contradiction is a dead end, a sign that the road leads nowhere and you should turn back and take the other road. A paradox, however, is an invitation to … Continue reading →

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Perfectness of the power graph

Posted on 04/10/2020 by Peter Cameron

The power graph of a group is the graph whose vertices are the group elements (sometimes the identity is excluded but it doesn’t matter here), in which x and y are joined if one is a power of the other. … Continue reading →

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On the Frattini subgroup

Posted on 07/09/2020 by Peter Cameron

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 →

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Surprising fun fact

Posted on 06/09/2020 by Peter Cameron

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 →

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Integrals of groups revisited

Posted on 04/09/2020 by Peter Cameron

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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A problem

Posted on 19/08/2020 by Peter Cameron

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 →

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