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dc.contributor.authorBächle, Andreas
dc.contributor.authorHerman, Allen
dc.contributor.authorKonovalov, Alexander
dc.contributor.authorMargolis, Leo
dc.contributor.authorSingh, Gurmail
dc.date.accessioned2018-04-05T23:34:40Z
dc.date.available2018-04-05T23:34:40Z
dc.date.issued2018
dc.identifier.citationBächle , A , Herman , A , Konovalov , A , Margolis , L & Singh , G 2018 , ' The status of the Zassenhaus conjecture for small groups ' Experimental Mathematics , vol. 27 , no. 4 , pp. 431-436 . https://doi.org/10.1080/10586458.2017.1306814en
dc.identifier.issn1058-6458
dc.identifier.otherPURE: 249587515
dc.identifier.otherPURE UUID: 94a52ebc-0708-4ade-a5eb-39c51e0e16fa
dc.identifier.otherRIS: urn:03AD99358E38DF12D905260DEACA2187
dc.identifier.otherScopus: 85017124889
dc.identifier.urihttp://hdl.handle.net/10023/13082
dc.description.abstractWe identify all small groups of order up to 288 in the GAP Library for which the Zassenhaus conjecture on rational conjugacy of units of finite order in the integral group ring cannot be established by an existing method. The groups must first survive all theoretical sieves and all known restrictions on partial augmentations (the HeLP+ method). Then two new computational methods for verifying the Zassenhaus conjecture are applied to the unresolved cases, which we call the quotient method and the partially central unit construction method. To the cases that remain we attempt an assortment of special arguments available for units of certain orders and the lattice method. In the end, the Zassenhaus conjecture is verified for all groups of order less than 144 and we give a list of all remaining cases among groups of orders 144 to 287.
dc.format.extent6
dc.language.isoeng
dc.relation.ispartofExperimental Mathematicsen
dc.rights© 2017, Taylor & Francis. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.tandfonline.com / https://doi.org/10.1080/10586458.2017.1306814en
dc.subjectIntegral group ringen
dc.subjectGroup of unitsen
dc.subjectZassenhaus conjectureen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleThe status of the Zassenhaus conjecture for small groupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.School of Computer Scienceen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1080/10586458.2017.1306814
dc.description.statusPeer revieweden
dc.date.embargoedUntil2018-04-05


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