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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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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

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