A Wilson Group of Non-Uniformly Exponential Growth

Details A Wilson Group of Non-Uniformly Exponential Growth A Wilson Group of Non-Uniformly Exponential Growth

2002-10-31

arxiv.org/abs/math/0210471v1

C. R. Math. Acad. Sci. Paris 336 (2003), no. 7, 549--554

Mathematics

Group Theory

6 pages, 2 figures

Scientific paper

10.1016/S1631-073X(03)00131-6

This note constructs a finitely generated group $W$ whose word-growth is exponential, but for which the infimum of the growth rates over all finite generating sets is 1 -- in other words, of non-uniformly exponential growth. This answers a question by Mikhael Gromov. The construction also yields a group of intermediate growth $V$ that locally resembles $W$ in that (by changing the generating set of $W$) there are isomorphic balls of arbitrarily large radius in $V$ and $W$'s Cayley graphs.

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