Cayley Graph Automatic Groups Are Not Necessarily Cayley Graph Biautomatic

  • Alexei Miasnikov
  • Zoran Šunić
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)


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


Automatic Structure Cayley Graph Automatic Group Cayley Graph Biautomatic Group Conjugacy Problem Isomorphism Problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexei Miasnikov
    • 1
  • Zoran Šunić
    • 2
  1. 1.Department of Mathematical SciencesStevens InstituteHobokenUSA
  2. 2.Department of MathematicsTexas A&M UniversityUSA

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