Galois coverings of Schreier graphs of groups generated by bounded automata

Abstract

We give a characterization of the covering Schreier graphs of groups generated by bounded automata to be Galois. We also investigate the zeta and L functions of Schreier graphs of few groups namely the Grigorchuk group, Gupta-Sidki p group, Gupta-Fabrykowski group and BSV torsion-free group.

27 pages, 12 figures, 3 tables. Major revision: improved exposition; the main theorem is strengthened to an if and only if statement; the paper has been streamlined and shortened