Tag Archives: permutation groups

Peter Neumann’s 3p paper

Posted on 15/04/2022 by Peter Cameron

In 1955, Helmut Wielandt published a paper proving the following theorem: Let G be a primitive permutation group of degree 2p, where p is a prime greater than 3, which is not doubly transitive. Then p = 2a2+2a+1 for some positive integer … Continue reading →

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Fair games and Artin’s conjecture

Posted on 10/04/2019 by Peter Cameron

A few years ago I described Persi Diaconis’ response to G. H. Hardy’s claim that there is a real dividing line between real and recreational mathematics. (See the report here.) This led from Persi’s first experiments in card shuffling to Artin’s conjecture … Continue reading →

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Books

Posted on 02/02/2019 by Peter Cameron

I realised yesterday that, although I had moved the web pages of books I had written to my St Andrews website when I came here, I had neither updated them nor put links to them. I have done the easier … Continue reading →

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Dugald Macpherson’s birthday meeting

Posted on 27/09/2018 by Peter Cameron

Still catching up on the backlog: last week I was in Edinburgh for a meeting at ICMS for Dugald Macpherson’s birthday. The ICMS has just moved to new premises at the top of the University of Edinburgh’s new Bayes Centre, … Continue reading →

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The existential transversal property

Posted on 21/08/2018 by Peter Cameron

One of the first things that João Araújo introduced me to when we started collaborating, after synchronization, was the universal transversal property: a permutation group G on the set {1,…,n} has the k-universal transversal property (k-ut for short) if, given … Continue reading →

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From permutation groups to model theory

Posted on 16/05/2018 by Peter Cameron

I cannot resist a conference with a title like this! But in this case, there is another very important reason to attend. In the mid-1970s, when I began being interested in infinite permutation groups (I had been a strictly finite … Continue reading →

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Symmetry vs Regularity

Posted on 06/12/2017 by Peter Cameron

This is the title of a conference to be held next year (2018) from 1 to 7 July, in Pilsen, Bohemia, Czech Republic. The subtitle is “The first 50 years since Weisfeiler-Leman stabilization”, and the webpage is here. If you … Continue reading →

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Summer school at Marienheide

Posted on 24/09/2017 by Peter Cameron

Last week, I was lecturing at a summer school in Franz Dohrmann Haus, a very pleasant conference centre in the small town of Marienheide, not far from Köln. Apart from a walk on Wednesday afternoon, I didn’t get much exercise, … Continue reading →

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A week in Vienna

Posted on 26/03/2017 by Peter Cameron

Last week, in the second week of Spring break in St Andrews, I was in Vienna, giving a course of lectures to the PhD students, at the invitation of Tomack Gilmore, a Queen Mary undergraduate now finishing his PhD with … Continue reading →

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12160

Posted on 27/10/2015 by Peter Cameron

12160 is an interesting number; but I didn’t know that until last night. As part of the work on semigroups, we are looking at the following problem. Given n and k, with n ≥ 2k, suppose that G is a k-homogeneous subgroup … Continue reading →

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