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Groups with a Recursively Enumerable Irreducible Word Problem

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Fundamentals of Computation Theory (FCT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8070))

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Abstract

The notion of the word problem is of fundamental importance in group theory. The irreducible word problem is a closely related concept and has been studied in a number of situations; however there appears to be little known in the case where a finitely generated group has a recursively enumerable irreducible word problem. In this paper we show that having a recursively enumerable irreducible word problem with respect to every finite generating set is equivalent to having a recursive word problem. We prove some further results about groups having a recursively enumerable irreducible word problem, amongst other things showing that there are cases where having such an irreducible word problem does depend on the choice of finite generating set.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Leicester, Leicester, LE1 7RH, U.K.

    Gabriela Aslı Rino Nesin & Richard M. Thomas

Authors
  1. Gabriela Aslı Rino Nesin
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  2. Richard M. Thomas
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Editor information

Editors and Affiliations

  1. Computer Science, University of Liverpool, Ashton Street, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Frank Wolter

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Rino Nesin, G.A., Thomas, R.M. (2013). Groups with a Recursively Enumerable Irreducible Word Problem. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-40164-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40163-3

  • Online ISBN: 978-3-642-40164-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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