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Transversals as Generating Sets in Finitely Generated Groups

dc.creatorButton, Jack
dc.creatorChiodo, Maurice Charles
dc.creatorLaris, Mariano Zeron-Medina
dc.date.accessioned2018-11-24T23:26:26Z
dc.date.available2015-07-10T11:40:37Z
dc.date.available2018-11-24T23:26:26Z
dc.date.issued2015-08-19
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/248887
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3826
dc.description.abstractWe explore transversals of finite index subgroups of finitely generated groups. We show that when H is a subgroup of a rank n group G and H has index at least n in G then we can construct a left transversal for H which contains a generating set of size n for G; this construction is algorithmic when G is finitely presented. We also show that, in the case where G has rank n ≤ 3, there is a simultaneous left-right transversal for H which contains a generating set of size n for G. We finish by showing that if H is a subgroup of a rank n group G with index less than 3⋅2^n-1, and H contains no primitive elements of G, then H is normal in G and G/H ≅ Cn2.
dc.languageen
dc.publisherCambridge University Press
dc.publisherBulletin of the Australian Mathematical Society
dc.rightshttp://creativecommons.org/licenses/by-nc/2.0/uk/
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales
dc.titleTransversals as Generating Sets in Finitely Generated Groups
dc.typeArticle


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