Discrete and free two-generated subgroups of SL2 over non-archimedean local fields

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dc.contributor.author Conder, Matthew J
dc.date.accessioned 2022-05-19T22:32:00Z
dc.date.available 2022-05-19T22:32:00Z
dc.date.issued 2020-7-1
dc.identifier.citation Journal of Algebra 553:248-267 01 Jul 2020
dc.identifier.issn 0021-8693
dc.identifier.uri https://hdl.handle.net/2292/59370
dc.description.abstract We present a practical algorithm which, given a non-archimedean local field K and any two elements A,B∈SL2(K), determines after finitely many steps whether or not the subgroup 〈A,B〉≤SL2(K) is discrete and free of rank two. This makes use of the Ping Pong Lemma applied to the action of SL2(K) by isometries on its Bruhat-Tits tree. The algorithm itself can also be used for two-generated subgroups of the isometry group of any locally finite simplicial tree, and has applications to the constructive membership problem. In an appendix joint with Frédéric Paulin, we give an erratum to his 1989 paper ‘The Gromov topology on R-trees’, which details some translation length formulae that are fundamental to the algorithm.
dc.language en
dc.publisher Elsevier BV
dc.relation.ispartofseries Journal of Algebra
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject Science & Technology
dc.subject Physical Sciences
dc.subject Mathematics
dc.subject Algorithm
dc.subject Groups acting on trees
dc.subject Frec
dc.subject Discrete
dc.subject EQUATION
dc.subject RANK
dc.subject math.GR
dc.subject math.GR
dc.subject math.GT
dc.subject 20E08
dc.subject 0101 Pure Mathematics
dc.title Discrete and free two-generated subgroups of SL2 over non-archimedean local fields
dc.type Journal Article
dc.identifier.doi 10.1016/j.jalgebra.2020.02.015
pubs.begin-page 248
pubs.volume 553
dc.date.updated 2022-04-04T02:01:27Z
dc.rights.holder Copyright: The author en
pubs.author-url http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000522801000009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e41486220adb198d0efde5a3b153e7d
pubs.end-page 267
pubs.publication-status Published
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article
pubs.subtype Journal
pubs.elements-id 830332
dc.identifier.eissn 1090-266X

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