On groups that have normal forms computable in logspace

Elder, M; Elston, G; Ostheimer, G

On groups that have normal forms computable in logspace

Elder, M

Elston, G Ostheimer, G

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Publication Type:: Journal Article
Citation:: Journal of Algebra, 2013, 381 pp. 260 - 281
Issue Date:: 2013-05-01

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	Elston, G	en_US
dc.contributor.author	Ostheimer, G	en_US
dc.date.issued	2013-05-01	en_US
dc.identifier.citation	Journal of Algebra, 2013, 381 pp. 260 - 281	en_US
dc.identifier.issn	0021-8693	en_US
dc.identifier.uri	http://hdl.handle.net/10453/98852
dc.description.abstract	We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite index subgroups, direct products, wreath products, and certain free products and infinite extensions, and includes the solvable Baumslag-Solitar groups, as well as non-residually finite (and hence non-linear) examples. We define a group to be logspace embeddable if it embeds in a group with normal forms computable in logspace. We prove that finitely generated nilpotent groups are logspace embeddable. It follows that all groups of polynomial growth are logspace embeddable. © 2013 Elsevier Inc.	en_US
dc.relation.ispartof	Journal of Algebra	en_US
dc.relation.isbasedon	10.1016/j.jalgebra.2013.01.036	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	On groups that have normal forms computable in logspace	en_US
dc.type	Journal Article
utslib.citation.volume	381	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	381	en_US

Abstract:

We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite index subgroups, direct products, wreath products, and certain free products and infinite extensions, and includes the solvable Baumslag-Solitar groups, as well as non-residually finite (and hence non-linear) examples. We define a group to be logspace embeddable if it embeds in a group with normal forms computable in logspace. We prove that finitely generated nilpotent groups are logspace embeddable. It follows that all groups of polynomial growth are logspace embeddable. © 2013 Elsevier Inc.

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http://hdl.handle.net/10453/98852