The automorphism group of Thompson's group F: subgroups and metric properties

Details The automorphism group of Thompson's group F: subgroups and metric properties The automorphism group of Thompson's group F: subgroups and metric properties

2011-07-21

arxiv.org/abs/1107.4336v1

Mathematics

Group Theory

24 pages, 14 figures

Scientific paper

We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective methods for estimating the word length of elements. We study some natural subgroups of Aut(F) and their metric properties. In particular, we show that the subgroup of inner automorphisms of F is at least quadratically distorted in Aut(F), whereas other subgroups of Aut(F) isomorphic to F are undistorted.

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