TY - JOUR
T1 - Groups whose word problems are not semilinear
AU - Gilman, Robert H.
AU - Kropholler, Robert P.
AU - Schleimer, Saul
N1 - Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - Suppose that G is a finitely generated group andWP(G) is the formal language ofwords 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 groupwhose graph lies in a certain infinite class, then WP(G) is not a multiple context-free language.
AB - Suppose that G is a finitely generated group andWP(G) is the formal language ofwords 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 groupwhose graph lies in a certain infinite class, then WP(G) is not a multiple context-free language.
KW - formal languages
KW - Group theory
KW - word problem
UR - http://www.scopus.com/inward/record.url?scp=85058059911&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85058059911&partnerID=8YFLogxK
U2 - 10.1515/gcc-2018-0010
DO - 10.1515/gcc-2018-0010
M3 - Article
AN - SCOPUS:85058059911
SN - 1867-1144
VL - 10
SP - 53
EP - 62
JO - Groups, Complexity, Cryptology
JF - Groups, Complexity, Cryptology
IS - 2
ER -