A Wilson Group of Non-Uniformly Exponential Growth
arXiv:math/0210471 · doi:10.1016/S1631-073X(03)00131-6
Abstract
This note constructs a finitely generated group 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 that locally resembles in that (by changing the generating set of ) there are isomorphic balls of arbitrarily large radius in and 's Cayley graphs.
6 pages, 2 figures