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- Title
Cross-wired lamplighter groups and linearity of automata groups.
- Authors
Ning Yang
- Abstract
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.
- Subjects
LINEAR systems; PROBABILISTIC automata; GROUP theory; NILPOTENT Lie groups; MATHEMATICAL proofs
- Publication
New York Journal of Mathematics, 2016, Vol 22, p379
- ISSN
1076-9803
- Publication type
Article