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Groups and semigroups with a one-counter word problem

By Derek F. Holt, Matthew D. Owens and R. M. Thomas

Abstract

We prove that a finitely generated semigroup whose word problem is a one-counter language has a linear growth function. This provides us with a very strong restriction on the structure of such a semigroup, which, in particular, yields an elementary proof of a result of Herbst, that a group with a one-counter word problem is virtually cyclic. We prove also that the word problem of a group is an intersection of finitely many one-counter languages if and only if the group is virtually abelian

Topics: QA
Publisher: Cambridge University Press
Year: 2008
OAI identifier: oai:wrap.warwick.ac.uk:861

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