A virtually 2-step nilpotent group with polynomial geodesic growth

Elder, M; Bishop, A

A virtually 2-step nilpotent group with polynomial geodesic growth

Elder, M

Bishop, A

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Publisher:: Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine
Publication Type:: Journal Article
Citation:: Algebra and Discrete Mathematics, 2022, 33, (2), pp. 21-21
Issue Date:: 2022-10-17

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945
dc.contributor.author	Bishop, A
dc.date.accessioned	2022-11-08T04:14:44Z
dc.date.available	2022-10-04
dc.date.available	2022-11-08T04:14:44Z
dc.date.issued	2022-10-17
dc.identifier.citation	Algebra and Discrete Mathematics, 2022, 33, (2), pp. 21-21
dc.identifier.issn	1726-3255
dc.identifier.issn	2415-721X
dc.identifier.uri	http://hdl.handle.net/10453/163315
dc.description.abstract	A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set.
dc.language	en
dc.publisher	Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine
dc.relation	http://purl.org/au-research/grants/arc/DP160100486
dc.relation.ispartof	Algebra and Discrete Mathematics
dc.relation.isbasedon	10.12958/adm1667
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	0101 Pure Mathematics
dc.title	A virtually 2-step nilpotent group with polynomial geodesic growth
dc.type	Journal Article
utslib.citation.volume	33
utslib.for	0101 Pure Mathematics
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.consider-herdc	true
dc.date.updated	2022-11-08T04:14:43Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	33
utslib.citation.issue	2

Abstract:

A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set.

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http://hdl.handle.net/10453/163315