Name
Abstract | ||
|---|---|---|
This paper investigates presentations of lamplighter groups using computational models from automata theory. The present work shows that if G can be presented such that the full group operation is recognised by a transducer, then the same is true for the lamplighter group
$$G \wr {{\mathbb {Z}}}$$
of G. Furthermore, Cayley presentations, where only multiplications with constants are recognised by transducers, are used to study generalised lamplighter groups of the form
$$G \wr {{\mathbb {Z}}}^d$$
and
$$G \wr F_d$$
, where
$$F_d$$
is the free group over d generators. Additionally,
$${{\mathbb {Z}}}_k \wr {{\mathbb {Z}}}^2$$
and
$${{\mathbb {Z}}}_k \wr {F_d}$$
are shown to be Cayley tree automatic. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s00236-022-00423-3 | Acta Informatica |
DocType | Volume | Issue |
Journal | 59 | 4 |
ISSN | Citations | PageRank |
0001-5903 | 0 | 0.34 |
References | Authors | |
12 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sanjay Jain | 1 | 1647 | 177.87 |
| Birzhan Moldagaliyev | 2 | 0 | 0.34 |
| Frank Stephan | 3 | 215 | 39.36 |
| Tien Dat Tran | 4 | 0 | 0.34 |