Thompson’s group F was introduced by Richard Thompson in the 1960’s and has since found applications in many areas of mathematics including algebra, logic and topology. We focus on the dead end depth of F, which is the minimal integer N such that for any group element, g, there is guaranteed to exist a path of length at most N in the Cayley graph of F leading from g to a point farther from the identity than g is. By viewing F as a diagram group, we improve the greatest known lower bound for the dead end depth of F with respect to the standard consecutive generating sets.

Faculty Advisor Name

Matthew Horak

Faculty Advisor Institution

University of Wisconsin–Stout

Suggested Mathematics Subject Classification(s)



This work was supported by NSF REU grant DMS 0453421.

Included in

Mathematics Commons



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