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BEING CAYLEY AUTOMATIC IS CLOSED UNDER TAKING WREATH PRODUCT WITH VIRTUALLY CYCLIC GROUPS

Part of: Theory of computing Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  13 April 2021

DMITRY BERDINSKY Open the ORCID record for DMITRY BERDINSKY [Opens in a new window] ,
MURRAY ELDER Open the ORCID record for MURRAY ELDER [Opens in a new window]  and
JENNIFER TABACK Open the ORCID record for JENNIFER TABACK [Opens in a new window]
DMITRY BERDINSKY
Affiliation:
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok10400, Thailand and Centre of Excellence in Mathematics, Commission on Higher Education, Bangkok 10400, Thailand e-mail: berdinsky@gmail.com
MURRAY ELDER*
Affiliation:
School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, NSW2007, Australia
JENNIFER TABACK
Affiliation:
Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, ME04011, USA e-mail: jtaback@bowdoin.edu
*
e-mail: murray.elder@uts.edu.au
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Abstract

We extend work of Berdinsky and Khoussainov [‘Cayley automatic representations of wreath products’, International Journal of Foundations of Computer Science27(2) (2016), 147–159] 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.

Keywords

Cayley automatic grouprestricted wreath productvirtually infinite cyclic grouplamplighter group

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 20E22: Extensions, wreath products, and other compositions 68Q45: Formal languages and automata
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 464 - 474
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was supported by Australian Research Council grant DP160100486. The third author acknowledges support from Simons Foundation grant 31736 to Bowdoin College.

References

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