### 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: doing mathematics

## 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

## Clive Sinclair

Yesterday I read the news that Clive Sinclair has died. This brought back memories of my first encounter with personal computers nearly 40 years ago. At the time I had a demanding job and three small children, and I was … Continue reading

Posted in doing mathematics, history, open problems
Tagged Neil Calkin, sum-free sets, ZX Spectrum
Leave a comment

## Graphs on groups, 8

The dark clouds seem to have lifted a bit. Perhaps now, that the last rush of conferences for a while is over, life can return to something like normality … For me the most significant event was the last in … Continue reading

Posted in doing mathematics, events, open problems
Tagged graphs and groups, matching number, power graph
3 Comments

## A new constant?

This is an appeal for help. Has anyone come across the constant 2.648102…? Here is the background, which connects with my previous posts about graphs on groups. We are interested in the clique number of the power graph of the … Continue reading

Posted in doing mathematics, open problems
Tagged clique number, Euler's function, power graph
8 Comments

## Graphs on groups, 2

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

Posted in doing mathematics, mathematics
Tagged commuting graph, enhanced power graph
Leave a comment

## Ramanujan+100

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

## 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