• Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: Finding short words in the first Grigorchuk group
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th Mar 2011
  • Abstract:

    In the 80's R.Grigorchuk found a finitely generated group such that the number of elements that can be written as a product of at most \(n\) generators grows faster than any polynomial in \(n\), but slower than any exponential in \(n\), so-called "intermediate" growth.

    It can be described as an group of automorphisms of an infinite rooted binary tree, or in terms of abstract computing devices called "non-initial finite transducers".

    In this talk I will describe what some of these short words/products of generators look like, and speculate on the asymptotic growth rate of all short words of length \(n\).

    This is joint unpublished work with Mauricio Gutierrez (Tufts) and Zoran Sunic (Texas A&M).

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