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 |
|