### Top Posts

### Recent comments

### Blogroll

- Astronomy Picture of the Day
- Azimuth
- British Combinatorial Committee
- Comfortably numbered
- Diamond Geezer
- Exploring East London
- From hill to sea
- Gödel's lost letter and P=NP
- Gil Kalai
- Jane's London
- Jon Awbrey
- Kourovka Notebook
- LMS blogs page
- Log24
- London Algebra Colloquium
- London Reconnections
- MathBlogging
- Micromath
- Neill Cameron
- neverendingbooks
- Noncommutative geometry
- numericana hall of fame
- Ratio bound
- Robert A. Wilson's blog
- Since it is not …
- Spitalfields life
- Sylvy's mathsy blog
- SymOmega
- Terry Tao
- The Aperiodical
- The De Morgan Journal
- The ICA
- The London column
- The Lumber Room
- The matroid union
- Theorem of the day
- Tim Gowers
- XKCD

### Find me on the web

### Cameron Counts: RSS feeds

### Meta

# Category Archives: exposition

## 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

Posted in doing mathematics, exposition
Tagged enhanced power graph, independence graph, power graph, rank, supersoluble group
1 Comment

## 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

Posted in doing mathematics, exposition
Tagged clique number, nilpotent group, solubility graph, souble group
Leave a comment

## 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

Posted in doing mathematics, exposition
Tagged 2-Engel group, commuting graph, conjugacy, Dedekind group, enhanced power graph, power graph
Leave a comment

## 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

Posted in doing mathematics, exposition, open problems
Tagged graph theory, group theory, number theory, open problems
Leave a comment

## Graphs on groups, 5

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 cograph, commuting graph, nilpotent group, perfect graph, power graph
2 Comments

## Oligomorphic groups: topology or geometry?

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

## A paradox, and where it led

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 Anti-foundation Axiom, Bea Adam-Day, random graph
Leave a comment

## Perfectness of the power graph

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 commuting graph, Lovász, partial preorder, perfect graph, power graph
1 Comment

## 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