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Groups with poly-context-free word problem
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Brough, Tara Rose (2010) Groups with poly-context-free word problem. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2491789~S15
Abstract
We call a language poly-context-free if it is an intersection of finitely many contextfree
languages. In this thesis, we consider the class of groups with poly-context-free
word problem. This is a generalisation of the groups with context-free word
problem, which have been shown by Muller and Schupp [17, 3] to be precisely the
finitely generated virtually free groups.
We show that any group which is virtually a finitely generated subgroup of a direct
product of finitely many free groups has poly-context-free word problem, and
conjecture that the converse also holds. We prove our conjecture for several classes
of soluble groups, including the metabelian groups and torsion-free soluble groups,
and present progress towards resolving the conjecture for soluble groups in general.
Some results in the thesis may be of independent interest in formal language theory
or group theory. In Chapter 2 we develop some tools for proving a language not to be
poly-context-free, and in Chapter 5 we prove that every finitely generated soluble
group which is not virtually abelian has a subgroup of one of a small number of
types.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mathematical linguistics | ||||
Official Date: | November 2010 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Holt, Derek F. | ||||
Sponsors: | University of Warwick | ||||
Extent: | ix, 110 leaves | ||||
Language: | eng |
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