South England Profinite Groups Meetings Joint Research Group funded by LMS Scheme 3 Academic Year 2007-08 This page keeps record of the meetings held during the year 2007-08. Please click here to move to events scheduled for this year. Background: In recent years profinite and asymptotic methods have been successfully applied to general problems of group theory. In addition there are interesting links to number theory and geometry. Activities: During the academic year 2007-08 we are holding a series of three meetings in order to - provide a platform for young mathematicians from across the south of England to meet and discuss their research in profinite groups, asymptotic group theory and related topics, - get graduate students and postdoctoral fellows involved by giving them the opportunity to discuss and possibly present their individual work, - give the participants an opportunity to widen their research horizons and their knowledge base by familiarising themselves with research adjacent to their own, - foster and develop collaborative links both within the group and with selected experts from the UK and abroad. Participants: We welcome and encourage interested mathematicians at all levels to join us in our meetings. The Joint Research Group receives financial support from the London Mathematical Society and has therefore limited funds to reimburse travel expenses of UK-based students and young mathematicians. Please contact the organisers if you wish to apply for such reimbursements. Organisers: Corresponding organisers of the Joint Research Group are Benjamin Klopsch (Royal Holloway, University of London), Nikolay Nikolov (Imperial College London) and Christopher Voll (University of Southampton).

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Next Meeting

There will be no more meetings this year. But we will apply for a renewal of the grant over the summer so that we can organise a similar series of meetings during the academic year 2008-09.
If you have any comments regarding past meetings or suggestions regarding future meetings, please let us know.

Many thanks to all participants and local organisers for making this series of events so successful!

Complete Calendar of Events

One-Day Meeting: The Nottingham Group - Recent Advances and Open Problems

• Description: The Nottingham group is the automorphism group of a local field of positive characteristic. It links the subject of profinite groups with number theory. The meeting will focus on recent advances by Mikhail Ershov and possible next steps.
• Location: Imperial College London
• Date: 8 December 2007
• Local Organiser: Nikolay Nikolov

Two-Day Workshop: The Algebraic Structure of Profinite Groups

• Description: Answering an old question of Jean-Pierre Serre, Nikolay Nikolov and Dan Segal recently proved that every subgroup of finite index in a finitely generated profinite group is automatically open. An essential concept in this context is verbal width, which was subsequently studied by Andrei Jaikin-Zapirain. The workshop will be build around these and related works.
• Location: Royal Holloway, University of London
• Date: 7-8 April 2008
• Local Organisers: Yiftach Barnea and Benjamin Klopsch

One-Day Meeting: Classification of Finite p-Groups by Coclass and Beyond

• Description: The classification of finite p-groups via coclass is one of the great success stories in applying profinite groups to general problems in group theory. A particular issue in this context is the periodicity in coclass graphs. This regular behaviour was first established by Marcus du Sautoy using p-adic integrals. More recently Bettina Eick and Charles Leedham-Green found an alternative, more constructive proof. The meeting will address these and related topics.
• Location: University of Cambridge
• Date: 11 July 2008
• Local Organiser: Rachel Camina

Past Meetings

Classification of Finite p-Groups by Coclass and Beyond

11 July 2008 at the University of Cambridge

• Description: The classification of finite p-groups via coclass is one of the great success stories in applying profinite groups to general problems in group theory. A particular issue in this context is the periodicity in coclass graphs. This regular behaviour was first established by Marcus du Sautoy using p-adic integrals. More recently Bettina Eick and Charles Leedham-Green found an alternative, more constructive proof. The meeting will address these and related topics.

  There were three longer and four shorter talks with breaks for discussions. The programme started at about 11:00 am and ended at about 5:30 pm. There were thirty participants. The titles of the talks were as follows (also see PDF file); those lecturers who gave computer presentation have kindly agreed to make available their slides.

  11.00 - 11.30 Introductory talk (Benjamin Klopsch)
  12.00 - 13.00 On the classification of p-groups by coclass: results and open problems (Bettina Eick; slides)
  14.00 - 15.00 Narrow graded Lie algebras (Sandro Mattarei; slides)
  15.30 - 16.15 Zeta functions of the coclass trees (Pirita Paajanen)
  16.45 - 17.00 Towards a classification of p-groups of maximal class using periodicity (Heiko Dietrich; slides)
  17.00 - 17.15 Applications of the classification of 2-groups by coclass (Dörte Feichtenschlager; slides)
  17.15 - 17.30 Periodicities in trees associated with the classification of p-groups by width, rank and obliquity (Tobias Rossmann; slides)

• Location: University of Cambridge
• Date: Friday, 11 July 2008
• Local Organiser: Rachel Camina

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The Algebraic Structure of Profinite Groups

7-8 April 2008 at Royal Holloway (University of London)

• Description: Answering an old question of Jean-Pierre Serre, Nikolay Nikolov and Dan Segal recently proved that every subgroup of finite index in a finitely generated profinite group is automatically open. An essential concept in this context is verbal width, which was subsequently studied by Andrei Jaikin-Zapirain. The workshop will be build around these and related works.
• Location: Royal Holloway, University of London
• Date: Monday and Tuesday, 7-8 April 2007
• Local Organisers: Yiftach Barnea and Benjamin Klopsch
• Further Information: Please visit the Workshop Web Page.

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The Nottingham Group - Recent Advances and Open Problems

Saturday, 8 December 2007 at Imperial College London

• Description: The Nottingham group is the automorphism group of a local field of positive characteristic. It links the subject of profinite groups with number theory. The meeting focused on recent advances by Mikhail Ershov and possible next steps.

  There were four talks with generous breaks for discussion. The programme started at 11:30 am and ended at about 6:00 pm. There were twenty participants. The titles and the speakers of the scheduled talks were:

  11.30 - 12.30 Introduction to the Nottingham group (Anton Evseev)
  13.30 - 14.30 Subgroups of the Nottingham Group (Benjamin Klopsch)
  15.30 - 16.30 Finite Presentation of the Nottingham Group (Susan McKay and Charles Leedham-Green)
  17.00 - 17.45 Commensurators of the Nottingham Group (Yiftach Barnea)

• Location: Imperial College London
• Date: Saturday, 8 December 2007
• Local Organiser: Nikolay Nikolov
• Resources: Here are some of the papers which formed a basis for the talks and discussions:
  - Y. Barnea and B. Klopsch, Index-subgroups of the Nottingham group, Adv. Math. 180 (2003), 187--221.
  - R. Camina, The Nottingham group, New horizons in pro-p groups, 205--221, Progr. Math. 184, Birkhäuser Boston, Boston, MA, 2000.
  - M. Ershov, New just-infinite pro-p groups of finite width and subgroups of the Nottingham group, J. Algebra 275 (2004), 419--449.
  - M. Ershov, The Nottingham group is finitely presented, J. London Math. Soc. (2) 71 (2005), 362--378.
  - S. McKay, Towards a finite presentation for the Nottingham group, J. Algebra 300 (2006), 316--338.

last significant update 12.09.2008
please bring corrections to the attention of Benjamin Klopsch