Cross-wired lamplighter groups and linearity of automata groups
Group Theory
2015-11-10 v1
Abstract
We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machine and cross-wired lamplighter groups. For a finite step two nilpotent group with central squares, we study its associated Cayley machine and give a presentation of the corresponding automata group. We show the automata group is a cross-wired lamplighter group and does not embed in the wreath product of a finite group with a torsion free group. For a subfamily of such finite step two nilpotent groups, we prove that their associated automata groups are linear.
Keywords
Cite
@article{arxiv.1511.02550,
title = {Cross-wired lamplighter groups and linearity of automata groups},
author = {Ning Yang},
journal= {arXiv preprint arXiv:1511.02550},
year = {2015}
}