Galois coverings of Schreier graphs of groups generated by bounded automata
Asif Shaikh, Daniele D'Angeli, Hemant Bhate, Dilip Sheth
TL;DR
This paper characterizes Galois coverings of Schreier graphs for groups generated by bounded automata and explores their zeta and L functions for specific groups like Grigorchuk and Gupta-Sidki.
Contribution
It provides a new characterization of Galois coverings of Schreier graphs and analyzes their zeta and L functions for notable automaton groups.
Findings
Characterization of Galois coverings of Schreier graphs
Analysis of zeta and L functions for specific groups
Insights into automaton-generated groups' graph structures
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Finite Group Theory Research