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Higher rank lamplighter groups are graph automatic. (English) Zbl 1427.20055

Summary: We show that the higher rank lamplighter groups, or Diestel-Leader groups \(\operatorname{\Gamma}_d(q)\) for \(d\geq 3\), are graph automatic. This introduces a new family of graph automatic groups which are not automatic.

MSC:

20F65 Geometric group theory
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
68Q45 Formal languages and automata
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