On a family of Schreier graphs of intermediate growth associated with a self-similar group

Details On a family of Schreier graphs of intermediate growth associated with a self-similar group On a family of Schreier graphs of intermediate growth associated with a self-similar group

2011-06-20

arxiv.org/abs/1106.3979v1

Mathematics

Group Theory

18 pages

Scientific paper

For every infinite sequence $\omega=x_1,x_2,...$, with $x_i\in\{0,1\}$, we construct an infinite 4-regular graph $X_{\omega}$. These graphs are precisely the Schreier graphs of the action of a certain self-similar group on the space $\{0,1\}^{\infty}$. We solve the isomorphism and local isomorphism problems for these graphs, and determine their automorphism groups. Finally, we prove that all graphs $X_\omega$ have intermediate growth.

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