Top Posts
Recent comments
 dsp on The enhanced power graph is weakly perfect
 dsp on The enhanced power graph is weakly perfect
 What Lovelace Did: From Bombelli to Bernoulli to Babbage  on Polynomials taking integer values
 What Ada Did: From Bombelli to Bernoulli to Babbage  on Polynomials taking integer values
 Peter Cameron on The enhanced power graph is weakly perfect
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

Join 659 other followers
Cameron Counts: RSS feeds
Meta
Category Archives: exposition
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 Antifoundation Axiom, Bea AdamDay, 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
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 nongenerators 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
5 Comments
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
Leave a comment
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
Leave a comment
Peter Sarnak’s Hardy Lecture
Yesterday, Peter Sarnak gave the London Mathematical Society’s 2020 Hardy Lecture (remotely). He talked about gaps in the spectra of connected cubic graphs. It was a talk properly described as a tour de force, applying to the problem ideas from … Continue reading
Posted in events, exposition
Tagged Alan Hoffman, fullerenes, generalised line graphs, Ramanujan graphs, spectral gaphs, waveguides
Leave a comment
The geometry of diagonal groups
This is an interim report on ongoing work with Rosemary Bailey, Cheryl Praeger and Csaba Schneider. We have reached a point where we have a nice theorem, even though there is still a lot more to do before the project … Continue reading
Posted in doing mathematics, exposition
Tagged Cartesian lattices, diagonal groups, partitions
8 Comments
The B. B. Newman Spelling Theorem
This is a guest post by CarlFredrik Nyberg Brodda, a recent Masters student at St Andrews and currently a PhD student at the University of East Anglia. The story has personal resonance for me, because it turns out that B. … Continue reading