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<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:14.0pt">This is the second and last announcement of<o:p></o:p></span></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">a mini workshop on <o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center"><b>"Finite groups and their automorphisms"<o:p></o:p></b></p>
<p class="MsoPlainText">which will take place in<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center"><b>Doğuş University, Istanbul, on August 10-12, 2015<o:p></o:p></b></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">following a course which will be delivered on <b>August 7-8, 2015
</b>by <b><o:p></o:p></b></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center"><b>Stefan Kohl <o:p>
</o:p></b></p>
<p class="MsoPlainText" align="center" style="text-align:center"><o:p> </o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center">"Introduction to GAP with an emphasis on automorphisms of finite groups".<o:p></o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center"><o:p> </o:p></p>
<p class="MsoPlainText" align="center" style="text-align:center"><o:p> </o:p></p>
<p class="MsoPlainText">The lectures will be given by<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"> <b>Marian Deaconescu</b>, An introduction to group actions.
<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"> <b>Gulin Ercan</b>, Frobenius-like groups as groups of automorphisms.<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"> <b>Stefan Kohl</b>, Finite groups and their automorphisms in GAP.<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"> <b>Pavel Shumyatsky</b>, On the length of a finite group.<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">There will be no other presentations. <o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">Participation is free, but the participants must care for their own lodging and boarding.
<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">If you would like<a name="_GoBack"></a> to attend the meeting you have to contact the organizing committee consisting of
<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"><b><span style="font-size:12.0pt"> Ismail Guloglu, Dogus University, Istanbul and<o:p></o:p></span></b></p>
<p class="MsoPlainText"><b><span style="font-size:12.0pt"> Fuat Erdem, Middle East Technical University, Ankara
<o:p></o:p></span></b></p>
<p class="MsoPlainText"><b><span style="font-size:12.0pt"><o:p> </o:p></span></b></p>
<p class="MsoPlainText">by sending an e-mail to <a href="mailto:iguloglu@dogus.edu.tr">
iguloglu@dogus.edu.tr</a><span class="MsoHyperlink"> <o:p></o:p></span></p>
<p class="MsoPlainText">or <a href="mailto:fuat.erdem@metu.edu.tr">fuat.erdem@metu.edu.tr</a>.<u><span style="color:blue"><o:p></o:p></span></u></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p class="MsoPlainText">The tentative program of the meeting and some details about the lectures as follows:<o:p></o:p></p>
<p class="MsoPlainText"><o:p> </o:p></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<b><span style="font-size:14.0pt;font-family:"Lucida Bright","serif";color:black;background:white">MINI COURSE by Stefan Kohl<o:p></o:p></span></b></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<b><span lang="EN-US" style="font-size:16.0pt;font-family:"Lucida Bright","serif";background:white">Introduction to GAP with an emphasis on automorphisms of finite groups<br>
</span></b><span lang="EN-US" style="font-size:9.0pt;font-family:"Lucida Console";background:white"><br>
</span><b><span style="font-size:11.0pt;font-family:"Lucida Bright","serif";background:white">Abstract.
</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">This minicourse provides the participants an introduction to GAP. They learn how to perform group theoretic computations in GAP, in particula</span><span style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">r
</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">such related to finite
<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">groups and their automorphisms.
<b>No prior knowledge of GAP is required.</b><i><o:p></o:p></i></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<b><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";background:white">Outline:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";background:white"> - overview of the GAP system: kernel, library,
documentation, data libraries, packages, etc.<br>
<br>
- 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<br>
<br>
- basics of the GAP programming language: data types,variables, expressions, statements, functions, operations, methods, etc.<br>
<br>
- the use of data libraries such as the Small Groups Library, the Transitive Groups Library etc.<br>
<br>
- possible ways to represent a group in GAP permutation groups, polycyclically presented groups, matrix groups, finitely presented groups etc.<br>
<br>
- computation of (and in) automorphism groups of groups;finding fixed subgroups of groups of automorphisms<br>
<br>
- the technique of switching to representations which are more suitable for particular computations via taking images and preimages under suitable isomorphisms<br>
-- this is relevant for computation in groups of automorphisms and many other kinds of groups<br>
<br>
- searching groups with particular group theoretic properties related to automorphisms in the Small Groups Library and other data libraries</span><b><u><span style="font-size:11.0pt;font-family:"Lucida Bright","serif""><o:p></o:p></span></u></b></p>
<p class="MsoNormal" style="text-align:justify"><b><u><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">Friday - August 7, 2015</span></u></b><u><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">
</span></u><u><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">10:30-11:20
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">11:40-12:30
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">LUNCH<o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">15:00-15:50
<b>Kohl<o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">16:10-17:00
<b>Kohl<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b><u><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">Saturday - August 8, 2015</span></u></b><u><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">10:30-11:20
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">11:40-12:30
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">LUNCH<o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="DE" style="font-size:12.0pt;font-family:"Cambria Math","serif"">15:00-15:50
<b>Kohl<o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">16:10-17:00
<b>Kohl<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b><u><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">Monday - August 10, 2015</span></u></b><u><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">
<o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">15:40-16:20
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">16:40-17:20
<b>Kohl<o:p></o:p></b></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span style="font-size:11.0pt;font-family:"Lucida Bright","serif";background:white"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="font-size:14.0pt;font-family:"Lucida Bright","serif";background:white">MINI-WORKSHOP
</span></b><b><span style="font-family:"Lucida Bright","serif";background:white"> on</span></b><span style="font-family:"Lucida Bright","serif";background:white">
</span><b><u><span style="font-size:14.0pt;font-family:"Cambria Math","serif"">FINITE GROUPS AND THEIR AUTOMORPHISMS</span></u></b><b><u><span lang="EN-US" style="font-size:14.0pt;font-family:"Cambria Math","serif""><o:p></o:p></span></u></b></p>
<p class="MsoNormal"><b><span style="font-size:14.0pt;font-family:"Lucida Bright","serif"">Abstracts of the Workshop Presentations<o:p></o:p></span></b></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<b><i><u><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">Marian Deaconescu</span></u></i></b><i><u><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">,
An introduction to group actions. <o:p></o:p></span></u></i></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">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.<br>
<br>
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.<br>
<br>
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?<br>
<br>
Applications to number theory will be also presented, including a characterization of the Mersenne primes. <br>
<br>
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...<br>
</span><span style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">------------------------------------------------------------------------------------------------------------------------------</span><i><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"><o:p></o:p></span></i></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"> <b><i><u>Gulin Ercan</u></i></b><i><u>, Frobenius-like groups as groups of automorphisms.
</u></i></span><i><u><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black"><o:p></o:p></span></u></i></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">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</span><span style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">
a continuation and generalization of the research of Khukhro, Makarenko and Shumyatsky about the
</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">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:<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">E.I.Khukhro,”Fitting height of a finite group with a Frobenius group of automorphisms”, J. Algebra 366, (2012), 1-11<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">G.Ercan,</span><span lang="EN-US" style="font-size:11.0pt;color:black">İ</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">.S.Güloglu,”<i>Action
of a Frobenius-like group</i>”, J. Algebra 402 (2014), 533-543<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">G.Ercan,</span><span lang="EN-US" style="font-size:11.0pt;color:black">İ</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">.S.Güloglu,
“<i>Action of a Frobenius-like group with fixed-point-free kernel</i>”,J.Group Theory 17 (2014),863-873<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">G.Ercan,</span><span lang="EN-US" style="font-size:11.0pt;color:black">İ</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black">.S.Güloglu,E.I.Khukhro”<i>Rank
and order of a finite group admitting a Frobenius-like group of automorphisms”, </i>
Algebra and Logic 53 (2014), 258-263<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<i><span style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white">-----------------------------------------------------------------------------------------------------------------------------------</span></i><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"> <o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"> <b><i><u>Pavel Shumyatsky</u></i></b><i><u>, On the length of a finite group.</u></i></span><i><u><span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black"><o:p></o:p></span></u></i></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"> 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.<o:p></o:p></span></p>
<p style="mso-margin-top-alt:10.5pt;margin-right:0cm;margin-bottom:10.5pt;margin-left:0cm;background:white">
<span lang="EN-US" style="font-size:11.0pt;font-family:"Lucida Bright","serif";color:black;background:white"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><u><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">Monday - August 10, 2015</span></u></b><u><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">
<o:p></o:p></span></u></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">10:30-11:20
<b>Deaconescu<o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">11:40-12:30
<b>Deaconescu<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">LUNCH<o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">14:30-15:20
<b>Ercan<o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">15:40-16:20
<b>Kohl <o:p></o:p></b></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif"">16:40-17:20
<b>Kohl<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b><u><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">Tuesday - August 11, 2015
</span></u></b><b><u><span lang="EN-US" style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p></o:p></span></u></b></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">10:30-11:20
<b>Deaconescu<o:p></o:p></b></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">11:40-12:30
<b>Deaconescu<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">LUNCH
</span></b><span style="font-size:12.0pt;font-family:"Cambria Math","serif""> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">14:30-15:20
<b>Shumyatsky</b> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">15:40-16:20
<b> Shumyatsky<o:p></o:p></b></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">16:40-17:20
<b>Ercan<o:p></o:p></b></span></p>
<p class="MsoNormal"><b><span style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></b></p>
<p class="MsoNormal"><b><u><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">Wednesday - August 12, 2015
<o:p></o:p></span></u></b></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">10:30-11:20
<b>Shumyatsky<o:p></o:p></b></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif"">11:40-12:30
<b>Shumyatsky<o:p></o:p></b></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Cambria Math","serif""><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:35.4pt"><o:p> </o:p></p>
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