Groups with a recursively enumerable irreducible word problem

Gabriela Rino Nesin, Richard M. Thomas

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBN

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.
Original languageEnglish
Title of host publicationInternational Symposium on Fundamentals of Computation Theory
Place of PublicationBerlin, Heidelberg
PublisherSpringer
Pages283-292
Number of pages10
Volume8070
DOIs
Publication statusPublished - 1 Jan 2013
EventInternational Symposium on Fundamentals of Computation Theory - Crowne Plaza Liverpool, 20 Aug 2013
Duration: 1 Jan 2013 → …

Publication series

NameLecture Notes in Computer Science

Conference

ConferenceInternational Symposium on Fundamentals of Computation Theory
Period1/01/13 → …

Bibliographical note

The final authenticated version is available online at https://doi.org/10.1007/978-3-642-40164-0_27

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