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

TL;DR

This paper proves that the property of being Cayley automatic remains intact when taking the restricted wreath product with a virtually infinite cyclic group, expanding the class of known Cayley automatic groups.

Contribution

It demonstrates that Cayley automaticity is preserved under wreath product with virtually cyclic groups, extending previous results in the field.

Findings

Cayley automatic groups are closed under wreath product with virtually cyclic groups.

The work generalizes known closure properties of Cayley automatic groups.

Adds new examples to the class of Cayley automatic groups.

Abstract

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