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# Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

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Volume 10, Issue 2

# Groups whose word problems are not semilinear

Robert H. Gilman
/ Robert P. Kropholler
/ Saul Schleimer
Published Online: 2018-10-30 | DOI: https://doi.org/10.1515/gcc-2018-0010

## Abstract

Suppose that G is a finitely generated group and $\mathrm{WP}\left(G\right)$ is the formal language of words defining the identity in G. We prove that if G is a virtually nilpotent group that is not virtually abelian, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then $\mathrm{WP}\left(G\right)$ is not a multiple context-free language.

Keywords: Group theory; formal languages; word problem

MSC 2010: 20F10; 68Q45

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Published Online: 2018-10-30

Published in Print: 2018-11-01

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1440140

This material is based upon work supported by the National Science Foundation grant DMS-1440140 while the authors were in residence at the Mathematical Science Research Institute (MSRI) in Berkeley, California, during the Fall 2016 Semester.

Citation Information: Groups Complexity Cryptology, Volume 10, Issue 2, Pages 53–62, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144,

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© 2018 Walter de Gruyter GmbH, Berlin/Boston.