Being Cayley automatic is closed under taking wreath product with\n virtually cyclic groups

2021/03/19 by Dmitry Berdinsky, Berdinsky, Dmitry, Murray Elder +3
Computer Science · Mathematics · #0F65 #20E22 #68Q45 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2103.10648

openalex publication_date 2021/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend work of the first author and Khoussainov to show that being Cayley\nautomatic is closed under taking the restricted wreath product with a virtually\ninfinite cyclic group. This adds to the list of known examples of Cayley\nautomatic groups.\n

Related

• Cayley automatic groups are not Cayley biautomatic
• Groups with a finite Busemann boundary are virtually cyclic
• The Cayley isomorphism property for Cayley maps
• Factor maps for automorphism groups via Cayley diagrams
• On the power graphs which are Cayley graphs of some groups