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Groups and semigroups with a one-counter word problem
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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 ISSN 1446-7887.
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Official URL: http://dx.doi.org/10.1017/S1446788708000864
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 | ||||
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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: |
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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 (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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