The distance of large $p$ th powers in the Nottingham group

Add to your list(s) Download to your calendar using vCal

• Tugba Aslan, Central European University
• Friday 27 November 2015, 15:00-16:00
• CMS, MR4.

If you have a question about this talk, please contact Nicolas Dupré.

The Nottingham group was introduced as a pro-$p$ group by D. Johnson and his Ph.D student I. York. Before then it was known by number theorists 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 characteristic. In other words, it is the group of formal power series with 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 $p$, contains an isomorphic copy of every finitely generated pro-$p$ group. Also, it has an important role in the theory of classification of just-infinite pro-$p$ groups, which are the simple objects in the category of pro-$p$ groups. The commutator structure of the Nottingham group is tight and well behaved. 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 of two elements of the Nottingham group, which was conjectured by K. Keating.

This talk is part of the Junior Algebra and Number Theory seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR4
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• Junior Algebra and Number Theory seminar
• School of Physical Sciences
• bld31
• ndb35's list

Note that ex-directory lists are not shown.