Show simple item record

dc.contributor.authorCamina, Rachel D.
dc.contributor.authorIñiguez, Ainhoa
dc.contributor.authorThillaisundaram, Anitha
dc.date.accessioned2020-11-18T16:18:57Z
dc.date.available2020-11-18T16:18:57Z
dc.date.issued2020-07-17
dc.date.submitted2020-05-14
dc.identifier.issn0003-889X
dc.identifier.others00013-020-01504-w
dc.identifier.other1504
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/313066
dc.descriptionFunder: University of Lincoln
dc.description.abstractAbstract: Let w be a word in k variables. For a finite nilpotent group G, a conjecture of Amit states that Nw(1)≥|G|k-1, where for g∈G, the quantity Nw(g) is the number of k-tuples (g1, …, gk)∈G(k) such that w(g1, …, gk)=g. Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit’s conjecture, which states that Nw(g)≥|G|k-1 for g a w-value in G, and prove that Nw(g)≥|G|k-2 for finite groups G of odd order and nilpotency class 2. If w is a word in two variables, we further show that the generalized Amit conjecture holds for finite groups G of nilpotency class 2. In addition, we use character theory techniques to confirm the generalized Amit conjecture for finite p-groups (p a prime) with two distinct irreducible character degrees and a particular family of words. Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.
dc.languageen
dc.publisherSpringer International Publishing
dc.rightsAttribution 4.0 International (CC BY 4.0)en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subjectArticle
dc.subjectWords
dc.subjectAmit’s conjecture
dc.subjectRational words
dc.subjectPrimary 20F10
dc.subjectSecondary 20D15
dc.titleWord problems for finite nilpotent groups
dc.typeArticle
dc.date.updated2020-11-18T16:18:56Z
prism.endingPage609
prism.issueIdentifier6
prism.publicationNameArchiv der Mathematik
prism.startingPage599
prism.volume115
dc.identifier.doi10.17863/CAM.60166
rioxxterms.versionofrecord10.1007/s00013-020-01504-w
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidThillaisundaram, Anitha [0000-0001-8768-2590]
dc.identifier.eissn1420-8938


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record

Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)