Metrics and embeddings of generalizations of Thompson's group F

Details Metrics and embeddings of generalizations of Thompson's group F Metrics and embeddings of generalizations of Thompson's group F

1998-09-30

arxiv.org/abs/math/9809185v3

Mathematics

Group Theory

16 pages, with figures created using pictex.tex under AMS-TeX, updated with more embeddings of F(p) into F(q)

Scientific paper

The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F(p). This interpretation of the metric is used to prove that every F(p) admits a quasi-isometric embedding into every F(q), and also to study the behavior of the shift maps under these embeddings.

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