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SUMMARY:The distance of large $p$ th powers in the Nottingham group - Tugb
 a Aslan\, Central European University
DTSTART:20151127T150000Z
DTEND:20151127T160000Z
UID:TALK62194@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:The Nottingham group was introduced as a pro-$p$ group by D. J
 ohnson and his Ph.D student I. York. Before then it was known by number th
 eorists as the group of normalized $F$ algebra automorphisms of the field 
 of fractions of the formal power series ring over the field $F$ of prime c
 haracteristic. In other words\, it is the group of formal power series wit
 h leading term $x$\, under formal substitution. Since being introduced as 
 a pro-$p$ group\, it has been investigated by many group theorists\, such 
 as\, A. Weiss\, C. Leedham-Green\, A. Shalev\, R. Camina\, Y. Barnea\, B. 
 Klopsch\, I. Fesenko\, M. Ershov\, C. Griffin\, P. Hegedus\, M. du Sautoy 
 and S. McKay. It gained interest as a pro-$p$ group after the result of R.
  Camina: The Nottingham group\, over a field of characteristic $p$\, conta
 ins an isomorphic copy of every finitely generated pro-$p$ group. Also\, i
 t has an important role in the theory of classification of just-infinite p
 ro-$p$ groups\, which are the simple objects in the category of pro-$p$ gr
 oups. The commutator structure of the Nottingham group is tight and well b
 ehaved. On the other hand\, the $p$ th powers drop quickly\, not yielding 
 any structure. In my talk\, after a survey about the Nottingham group and 
 pro-$p$ groups in general\, I will introduce a matrix (which was initially
  defined by K. Keating) to compute a certain type of commutator.  It has a
  key role to prove a sharp bound for the distance of higher $p$ th powers 
 \nof two elements of the Nottingham group\, which was conjectured by K. Ke
 ating.
LOCATION:CMS\, MR4
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