Author Archives: Evgeny Khukhro

Call for new Kourovka problems in Group Theory

Evgeny Khukhro announced koura start for preparation of the new 19th edition of the Kourovka Notebook” — the famous collection of unsolved problems in Group Theory and related areas. This publication originated in Novosibirsk in 1965, since then gained world-wide popularity and now includes more than 1000 problems by about 400 authors from all over the world. Nowadays it is published on the web but still retains discrete issues appearing every 3–4 years, with more frequent updates online.

For more than 50 years the “Kourovka Notebook” has served as a unique means of communication for researchers in Group Theory and nearby fields of mathematics. Maybe the most striking illustration of its success is the fact that more than 3/4 of the problems from the first issue have now been solved! (Of course, it is often easier to propose a new problem than to solved an old one…)

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 would be “measured” and seen, the preference is usually given to concrete questions that admit “yes” or “no” answers.

The Editors also welcome any other comments on, or/and solutions of, existing problems; the current version on Arxiv incorporates all comments so far.

The problems and comments can be sent to any of the Editors (preferably by e-mail):

Evgeny Khukhro khukhro@yahoo.co.uk or Victor Mazurov mazurov@math.nsc.ru

 

Algebraic conference in Lincoln

confSchool of Mathematics and Physics conducted the conference “Maximal Conditions and Embeddings of Profinite Groups” in University of Lincoln on 2nd June. The conference was supported by a grant of the London Mathematical Society under the ‘Celebrating New Appointments’ scheme, which was secured by Dr Anitha Thilaisundaram.  The participants included Prof Dugald Macpherson (Leeds), Prof Rögnvaldur G. Möller (University of Iceland, Reykjavik), Prof Peter Neumann (Oxford), Prof Dan Segal (Oxford), Prof John Wilson (Oxford), as well as young researchers from Australia, Germany, and UK. The talks were given by Alejandra Garrido (Düsseldorf), Simon Smith (Lincoln), Anitha Thillaisundaram (Lincoln), and John Wilson (Oxford); see the programme here.

After the conference a wine reception was addressed by the Pro Vice Chancellor of UoL / Head of College of Science and Engineering Prof Libby John and Prof John Wilson (Oxford). The reception was followed by the conference dinner.

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Two talks at LARA seminar by Prof Rögnvaldur G. Möller and by Dr Colin Reid

Another enhanced Lincoln Algebra Research Afternoon (LARA) before the conference “Maximal Conditions and Embeddings of Profinite Groups” on 2nd June. On 31th of May we had two talks:

Prof Rögnvaldur G. Möller (University of Iceland), Minimal valency of a Cayley–Abels graph and group properties, 

Dr Colin Reid (ARC DECRA Fellow at University of Newcastle, Australia), Chief series of locally compact groups. 

 

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Prof R. G. Möller 

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Dr C. Reid 

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LARA seminar by Dr Alejandra Garrido

On 30th of May we had a P1030268aseminar within the Lincoln Algebra Research Afternoons (LARA), with Dr Alejandra Garrido (currently an Alexander von Humboldt research fellow at Duesseldorf) giving a talk on Congruence and profinite completions for groups acting on rooted treesP1030280aP1030261a

The next LARA seminar will be on 31st May 2017 with two talks, one by Röggi Möller (Univ. of Iceland), and another by Colin Reid (Newcastle Univ., Australia).

We enjoy several extra speakers at LARA seminars due to participants arriving in Lincoln for the forthcoming conference “Maximal Conditions and Embeddings of Profinite Groups” on 2nd June.

Visiting Isaac Newton’s birthplace

Maths & Physics News

On 26 May our maths and physics students and staff visited Woolsthorpe Manor — the birthplace of Isaac Newton, where he also spent much time in 1665-67 making  most important discoveries in maths and physics, in particular, laying foundations of Calculus, conducting experiments with light. Here still grows the famous apple tree, the falling of apples of which Newton used to illustrate his theory of gravitation. A story of Newton’s life was presented by a National Trust volunteer, followed by a short talk on Newton’s mathematics by Dr Evgeny Khukhro. After Woolsthorpe Manor, the day trip was continued with a visit to Belton House and gardens.

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LARA seminar by Sandro Mattarei

On 16th of May reciprwe had a seminar within the Lincoln Algebra Research Afternoons (LARA), with Sandro Mattarei reporting on his recent work on Generalizations of self-reciprocal polynomials.

The next LARA seminar will be delivered on 30th May 2017 by Dr Alejandra Garrido (Duesseldorf), as part of her visit to Lincoln for the forthcoming conference “Maximal Conditions and Embeddings of Profinite Groups” .

Visit by Professor Andrei Jaikin-Zapirain

Professor Andrei Jaikin-Zapirain P1030187a(Autonomous University of Madrid, currently at University of Oxford) visited Lincoln School of Mathematics and Physics on 10 May 2017. He gave a talk “On l2-Betti numbers and their analogues in positive characteristicat the Algebra research seminar (Abstract)P1030181abbb P1030179a

New paper accepted in Journal of Algebra

The paper JA-coverby Evgeny Khukhro and Pavel Shumyatsky “Almost Engel compact groups”http://dx.doi.org/10.1016/j.jalgebra.2017.04.021, has just been accepted for publication in Journal of Algebra.

(See also https://arxiv.org/pdf/1610.02079.pdf.)

Abstract: We say that a group G is almost Engel if for every g\in G there is a finite set {\mathscr E}(g) such that for every x\in G all sufficiently long commutators [...[[x,g],g],\dots ,g] belong to {\mathscr E}(g), that is, for every  x\in G there is a positive integer n(x,g) such that [...[[x,g],g],\dots ,g]\in {\mathscr E}(g) if g is repeated at least n(x,g) times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose {\mathscr E}(g)=\{ 1\} for all $g\in G$.) We prove that if a compact (Hausdorff) group G is almost Engel, then G has a finite normal subgroup N such that G/N is locally nilpotent. If in addition there is a unform bound |{\mathscr E}(g)|\leq m for the orders of the corresponding sets, then the subgroup N can be chosen of order bounded in terms of m. The proofs use the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent.

 

Visit by Dr Rachael Camina

P1020968aDr Rachel Camina (University of Cambridge)  visited School of Mathematics and Physics on  29 March 2017. She gave a talk “Vanishing Class Sizes” at the Algebra research seminar. P1020977a

Anita Thillaisundaram in Women in Maths.

Maths & Physics News

University of Lincoln Lecturer, Anita Thillaisundaram has been featured in Women in Maths.

To read more, click the link here. Congratulations, Anitha!

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