Tag Archives: CFSG

A small problem

In connection with the research discussion about graphs and groups, I began to wonder which finite groups have the property that any two elements of the same order are conjugate. I thought about this, and got a certain distance, and … Continue reading

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Prospects in Mathematics, 2

I didn’t say anything about my own talk at the Prospects in Mathematics meeting. But soon afterwards I was re-reading Lee Smolin’s 2006 book The Trouble with Physics, and it resonated with some of the things I said. My topic … Continue reading

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Commuting graph, 2

Last week Chris Parker gave a very interesting talk in the London Algebra Colloquium on this topic. It is an excellent example of a curious phenomenon. If you look for your keys under the lamppost, then in a Borgesian way … Continue reading

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Finding derangements without CFSG

Nearly two years ago, I posed the problem of finding an “elementary” deterministic polynomial-time algorithm for finding a fixed-point-free element (or derangement) in a transitive permutation group. The background is that there are so many fpf elements (at least a … Continue reading

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Finite simple groups

The blog Gödel’s Last Letter and P=NP is always worth reading. The two bloggers, RJ Lipton and KW Regan, are computer scientists, but they have interesting things to say about developments in mathematics, and other areas too. For example, last year they … Continue reading

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A permutation group challenge, 3

“Then I will do it myself”, said the little red hen. And she did. Since nobody took up the challenge, I had to do it myself. Let λ be a partition of n. We say that a permutation group G … Continue reading

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A permutation group challenge

Long ago, in the distant past before the Classification of Finite Simple Groups, Peter Neumann, Jan Saxl and I investigated the class of permutation groups acting on sets of even cardinality n = 2k, with the following interchange property: Any subset of … Continue reading

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35ACCMCC at Monash

I’ve just spent a week at the 35th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing at Monash University in Clayton, a suburb of Melbourne. The conference happened to coincide with a research visit to Monash, about which I will … Continue reading

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