Category Archives: exposition

a post aimed to teach something

Hall’s Marriage Theorem

Posted on 27/03/2020 by

Philip Hall was one of the greatest group theorists of the twentieth century. But it may well be that he is known to more people for a result which on the face of it is pure combinatorics, with nothing to … Continue reading →

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Research trips in February

Posted on 13/03/2020 by

I don’t know how things have got so busy. I had two interesting trips in February; I worked hard, and some interesting mathematics resulted; but I don’t seem to have found the time to describe it. So here goes. This … Continue reading →

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GRA workshop 2

Posted on 31/01/2020 by

This workshop was on “Computational and algorithmic aspects” (of groups, representations and applications, presumably). In my opinion, this was the week when the programme really took off. There were many good talks, so as ever I shall just select a … Continue reading →

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GRA Workshop 1

Posted on 15/01/2020 by

Last week was the introductory/instructional workshop for the Isaac Newton Institute’s six-month programme on Groups, Representations and Applications. We were thrown in the deep end right at the start. The first two talks were on what were claimed to be … Continue reading →

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The Frattini argument

Posted on 02/01/2020 by

The Frattini subgroup of a finite group G can be defined in two equivalent ways: it is the intersection of all the maximal proper subgroups of G; it is the set of all non-generators of G, that is, elements which … Continue reading →

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Sylow’s Theorem, from the book

Posted on 22/12/2019 by

The most important theorems of elementary group theory are those of Lagrange and Sylow. I want to describe here what I consider the most beautiful proof of the first part of Sylow’s Theorem, actually based on Sylow’s original proof. But … Continue reading →

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Something I didn’t know

Posted on 09/11/2019 by

I didn’t know this, though probably I should have. Maybe you didn’t know it either. We work in a semigroup, a system with an operation (called multiplication) satisfying the associative law. A generalised inverse of an element A is an … Continue reading →

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