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Author Archives: Peter Cameron
A rant
When the Great Helmsman died in 1976, Jung Chang was able to put on a convincing display of abandoned grief. But afterwards, she decided to think through Mao’s philosophy, and how he had been able to exert such control. She … 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
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Between Fermat and Mersenne
The following problem came up in something I was doing recently. I have no idea how difficult it is – it looks hard to me – but I would be glad to hear from anyone who knows more than I … Continue reading
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
Permanence of open access publication
Both email accounts I use have rather zealous spam filters, and from time to time I have to check what they have filtered out. (An excuse for slow response to email?) The last time I looked I found a copy … Continue reading
Combinatorial Theory
I learned yesterday of a new free and open-access journal, Combinatorial Theory, owned by its editorial board. There is a temporary web page here, on which the editorial board (including some familiar names) is listed. This journal joins a list … Continue reading
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 non-generators 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
4 Comments
