On 18th October, Simon Smith gave a talk at the Algebra and Representation Theory Seminar at the University of Cambridge, on his recent results about the structure of profinite groups that can be embedded as a maximal open subgroup in some larger topological group.

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On Wednesday the 18th of October 2017, Anitha Thillaisundaram spoke on branch groups at the Pure Mathematics Colloquium of Lancaster University.

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The new “Research Highlights 2015–2017” brochure has now been printed. This booklet contains brief descriptions of some of the best achievements of the…]]>

The new “Research Highlights 2015–2017” brochure has now been printed. This booklet contains brief descriptions of some of the best achievements of the members of staff of School of Mathematics and Physics over the last couple of years, as well as reports on the first mathematics conference in Lincoln and the graduation in 2016.

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Florian Lehner from the University of Warwick visited the University of Lincoln School of Mathematics and Physics this week, to work on a joint research project with Simon Smith. The project involves breaking the symmetries of infinite graphs by colouring the vertices, and in particular studying the minimum density of any such colouring.

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The preparation of the new 19th edition of the “Kourovka Notebook” in underway. Everybody is welcome to propose new problems to be included in the new edition. Problems may “belong” to those who propose them, or otherwise. In the latter case, one can indicate the author(s) of the problem (if different from the person proposing), or simply that this is a “well-known problem”. In order that the progress could be “measured” and seen, the preference is usually given to concrete questions that admit “yes” or “no” answers.

We also welcome any other comments on or/and solutions of existing problems.

The problems can be sent to the editors (preferably by e-mail): Evgeny Khukhro khukhro@yahoo.co.uk and Victor Mazurov mazurov@math.nsc.ru .

A new update for the current 18th edition of “Kourovka Notebook (Unsolved Problems in Group Theory)” has been posted. All the changes (a few new and old solutions, corrections, new references, etc.) are incorporated in the new version of the main PDF file at http://arxiv.org/abs/1401.0300 . In addition, for convenience of the readers, all the changes made since the 18th edition first appeared are also listed separately here.

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(See also https://arxiv.org/pdf/1609.07677.pdf.)

*Abstract*: A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz’s formula extends, essentially without change, to a count of irreducible polynomials arising through an arbitrary quadratic transformation. In the present paper we provide an explanation for this extension, and a simpler proof of Ahmadi’s result, by a reduction to the known special case of self-reciprocal polynomials and a minor variation. We also prove further results on polynomials arising through a quadratic transformation, and through some special transformations of higher degree.

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