New York Journal of Mathematics
Volume 22 (2016) 379-404


Ning Yang

Cross-wired lamplighter groups and linearity of automata groups

view    print

Published: April 20, 2016
Keywords: automata groups, Cayley machine, cross-wired lamplighter groups, wreath products, linearity
Subject: 20E08, 20E22, 20G15

We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machines 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.

Author information

Department of Mathematics, Indiana University -- Bloomington, Rawles Hall, Bloomington, IN 47405, USA