Holt, Derek F., Owens, Matthew D. and Thomas, R. M. (2008) Groups and semigroups with a one-counter word problem. Journal of the Australian Mathematical Society, Vol.85 (No.2). pp. 197-209. doi:10.1017/S1446788708000864

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Word problems (Mathematics), Semigroup, Finite groups, Abelian groups, Group theory
Journal or Publication Title:	Journal of the Australian Mathematical Society
Publisher:	Cambridge University Press
ISSN:	1446-7887
Official Date:	October 2008
Dates:	Date Event October 2008 Published
Volume:	Vol.85
Number:	No.2
Number of Pages:	13
Page Range:	pp. 197-209
DOI:	10.1017/S1446788708000864
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access

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