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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2012, Volume 14, Issue 2, Pages 185–216 (Mi adm93)

RESEARCH ARTICLE

Word length in symmetrized presentations of Thompson's group $F$

Matthew Horaka, Alexis Johnsonb, Amelia Stonesiferc

a University of Wisconsin-Stout, Menomonie, WI 54751, USA
b Grand Valley State University, Allendale, MI 49401-9403, USA
c St. Olaf College, Northfield, Minnesota 55057, USA

Abstract: Thompson's groups $F, T$ and $Z$ were introduced by Richard Thompson in the 1960's in connection with questions in logic. They have since found applications in many areas of mathematics including algebra, logic and topology, and their metric properties with respect to standard generating sets have been studied heavily. In this paper, we introduce a new family of generating sets for $F$, which we denote as $Z_n$, establish a formula for the word metric with respect to $Z_1$ and prove that $F$ has dead ends of depth at least $2$ with respect to $Z_1$.

Keywords: Thompson's group $F$, dead ends, diagram group.

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Bibliographic databases:
MSC: 20F65
Revised: 07.09.2012
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Citation: Matthew Horak, Alexis Johnson, Amelia Stonesifer, “Word length in symmetrized presentations of Thompson's group $F$”, Algebra Discrete Math., 14:2 (2012), 185–216

Citation in format AMSBIB
\Bibitem{HorJohSto12} \by Matthew~Horak, Alexis~Johnson, Amelia~Stonesifer \paper Word length in symmetrized presentations of Thompson's group $F$ \jour Algebra Discrete Math. \yr 2012 \vol 14 \issue 2 \pages 185--216 \mathnet{http://mi.mathnet.ru/adm93} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3099969} \zmath{https://zbmath.org/?q=an:1288.20052}