[Turkmath:612] 2.announcement

Tue Jul 28 08:18:31 UTC 2015

This is the second and last announcement of

a mini workshop on

"Finite groups and their automorphisms"

which will take place in

Doğuş University, Istanbul, on August 10-12, 2015

following a course which will be delivered on August 7-8, 2015 by

Stefan Kohl

"Introduction to GAP with an emphasis on automorphisms of finite groups".

The lectures will be given by

   Marian Deaconescu, An introduction to group actions.

   Gulin Ercan, Frobenius-like groups as groups of automorphisms.

   Stefan Kohl, Finite groups and their automorphisms in GAP.

   Pavel Shumyatsky, On the length of a finite group.

There will be no other presentations.

Participation is free, but the participants must care for their own lodging and boarding.

If you would like to attend the meeting you have to contact the organizing committee consisting of

  Ismail Guloglu, Dogus University, Istanbul and

  Fuat Erdem, Middle East Technical University, Ankara

by sending an e-mail to iguloglu at dogus.edu.tr<mailto:iguloglu at dogus.edu.tr>

or fuat.erdem at metu.edu.tr<mailto:fuat.erdem at metu.edu.tr>.

The tentative program of the meeting and some details about the lectures as follows:

MINI COURSE  by Stefan Kohl

Introduction to GAP with an emphasis on automorphisms of finite groups

Abstract. This minicourse provides the participants an introduction to GAP. They learn how to perform group theoretic computations in GAP, in particular such related to finite

groups and their automorphisms. No prior knowledge of GAP is required.

Outline: - overview of the GAP system: kernel, library, documentation, data libraries, packages, etc.

   - interactive use of GAP: the read-eval-view loop; session log files; reading in GAP code and data from a file, writing data to a file

   - basics of the GAP programming language: data types,variables, expressions, statements, functions, operations, methods, etc.

   - the use of data libraries such as the Small Groups Library, the Transitive Groups Library etc.

   - possible ways to represent a group in GAP permutation groups, polycyclically presented groups, matrix groups, finitely presented groups etc.

   - computation of (and in) automorphism groups of groups;finding fixed subgroups of groups of automorphisms

   - the technique of switching to representations which are more suitable for particular computations via taking images and preimages under suitable isomorphisms
     -- this is relevant for computation in groups of automorphisms and many other kinds of groups

   - searching groups with particular group theoretic properties related to automorphisms in the Small Groups Library and other data libraries
Friday - August 7, 2015
10:30-11:20         Kohl
11:40-12:30         Kohl
LUNCH
15:00-15:50          Kohl
16:10-17:00          Kohl

Saturday - August 8, 2015
10:30-11:20          Kohl
11:40-12:30          Kohl
LUNCH
15:00-15:50          Kohl
16:10-17:00          Kohl

Monday - August 10, 2015
15:40-16:20           Kohl
16:40-17:20           Kohl

MINI-WORKSHOP  on  FINITE GROUPS AND THEIR AUTOMORPHISMS
Abstracts of the Workshop Presentations

Marian Deaconescu, An introduction to group actions.

My lectures will focus on some of the most general (you might read ''shallow'', or, ''not deep'', or ''elementary'') aspects of the action of a finite group A which acts via automorphisms on a finite group G.

I think that, today, the general theory (in the context described above) is in its infancy and I am ready to babble something on these lines.

I plan to start from first principles, giving (?) boring proofs of three lines, and finishing with things (yes, elementary mathematics can be surprising) that give an answer to an old problem (no, not an ''old open question'', for nobody believed that this question could be ever answered...) that preoccupied both Dedekind and Frobenius around 1890: when is a product of two commutators in a finite group again a commutator?

Applications to number theory will be also presented, including a characterization of the Mersenne primes.

I am ''old school'' , I will write on a board (with aiding notes and glasses at hand), so please bring your pens and your notebooks...
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  Gulin Ercan, Frobenius-like groups as groups of automorphisms.

These talks will discuss some developments about the structure of finite groups admitting a Frobenius-like group as a group of automorphisms. This is essentially a continuation and generalization of the research of Khukhro, Makarenko and Shumyatsky about the structure of finite groups admitting a Frobenius group as a group of automorphisms. For a first reading of the already realized research on that subject one can consult the papers:

E.I.Khukhro,"Fitting height of a finite group with a Frobenius group of automorphisms", J. Algebra 366, (2012), 1-11

G.Ercan,İ.S.Güloglu,"Action of a Frobenius-like group", J. Algebra 402 (2014), 533-543

G.Ercan,İ.S.Güloglu, "Action of a Frobenius-like group with fixed-point-free kernel",J.Group Theory 17 (2014),863-873

G.Ercan,İ.S.Güloglu,E.I.Khukhro"Rank and order of a finite group admitting a Frobenius-like group of automorphisms", Algebra and Logic 53 (2014), 258-263

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 Pavel Shumyatsky, On the length of a finite group.

 Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. The nonsoluble length of G  is defined as the minimum number of nonsoluble factors in a series of this kind. Upper bounds for the nonsoluble length appear in the study of various problems on finite, residually finite, and profinite groups. In particular, such bounds played important role in the Hall-Higman reduction theorem for the restricted Burnside problem. In the talk several new results on nonsoluble length will be discussed. Most of the results were obtained during recent collaboration with Khukhro.

Monday - August 10, 2015
10:30-11:20          Deaconescu
11:40-12:30          Deaconescu
LUNCH
14:30-15:20          Ercan
15:40-16:20           Kohl
16:40-17:20           Kohl

Tuesday - August 11, 2015
10:30-11:20           Deaconescu
11:40-12:30           Deaconescu
LUNCH
14:30-15:20          Shumyatsky
15:40-16:20          Shumyatsky
16:40-17:20          Ercan

Wednesday - August 12, 2015
10:30-11:20           Shumyatsky
11:40-12:30           Shumyatsky

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