Category Archives: exposition

a post aimed to teach something

Graphs on groups, 12

Posted on 03/01/2022 by Peter Cameron

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 →

Posted in doing mathematics, exposition | Tagged , , , , | 1 Comment

Graphs on groups, 11

Posted on 02/01/2022 by Peter Cameron

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 →

Posted in doing mathematics, exposition | Tagged , , , | Leave a comment

Graphs on groups, 10

Posted on 01/01/2022 by Peter Cameron

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 →

Posted in doing mathematics, exposition | Tagged , , , , , | Leave a comment

Graphs on groups, 9

Posted on 08/11/2021 by Peter Cameron

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 →

Posted in doing mathematics, exposition, open problems | Tagged , , , | Leave a comment

Graphs on groups, 5

Posted on 26/03/2021 by Peter Cameron

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 →

Posted in events, exposition, open problems | Tagged , , , , | 2 Comments

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 →

Posted in doing mathematics, exposition, open problems | Tagged , , , | 2 Comments

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 →

Posted in doing mathematics, exposition | Tagged , , , , , , , , | 2 Comments

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 →

Posted in doing mathematics, exposition | Tagged , , | Leave a comment

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 →

Posted in doing mathematics, exposition | Tagged , , , , | 1 Comment

The Fitting subgroup

Posted on 14/09/2020 by Peter Cameron

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