Cayley automatic groups are not Cayley biautomatic

Abstract

We show that there are Cayley automatic groups that are not Cayley biautomatic. In addition, we show that there are Cayley automatic groups with undecidable Conjugacy Problem and that the Isomorphism Problem is undecidable in the clas of Cayley automatic groups.

References in corpus (2)

• Unsolvability of the isomorphism problem for [free abelian]-by-free groups
• The conjugacy problem in automaton groups is not solvable