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Some isomorphism results for Thompson-like groups Vn(G)
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dc.contributor.author | Bleak, Collin | |
dc.contributor.author | Donoven, Casey | |
dc.contributor.author | Jonusas, Julius | |
dc.date.accessioned | 2018-11-08T00:49:33Z | |
dc.date.available | 2018-11-08T00:49:33Z | |
dc.date.issued | 2017-11-08 | |
dc.identifier | 231626997 | |
dc.identifier | 75d4b789-f1b5-4d9d-8350-db70252b6b58 | |
dc.identifier | 85035039509 | |
dc.identifier | 000415653400001 | |
dc.identifier.citation | Bleak , C , Donoven , C & Jonusas , J 2017 , ' Some isomorphism results for Thompson-like groups V n (G) ' , Israel Journal of Mathematics , vol. 222 , no. 1 , pp. 1-19 . https://doi.org/10.1007/s11856-017-1580-5 | en |
dc.identifier.issn | 0021-2172 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1410.8726v2 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/73701274 | |
dc.identifier.uri | https://hdl.handle.net/10023/16413 | |
dc.description.abstract | We find some perhaps surprising isomorphism results for the groups {Vn(G)}, where Vn(G) is a supergroup of the Higman–Thompson group Vn for n ∈ N and G ≤ Sn, the symmetric group on n points. These groups, introduced by Farley and Hughes, are the groups generated by Vn and the tree automorphisms [α]g defined as follows. For each g ∈ G and each node α in the infinite rooted n-ary tree, the automorphisms [α]g acts iteratively as g on the child leaves of α and every descendent of α. In particular, we show that Vn ≅ Vn(G) if and only if G is semiregular (acts freely on n points), as well as some additional sufficient conditions for isomorphisms between other members of this family of groups. Essential tools in the above work are a study of the dynamics of the action of elements of Vn(G) on the Cantor space, Rubin’s Theorem, and transducers from Grigorchuk, Nekrashevych, and Suschanskiĭ’s rational group on the n-ary alphabet. | |
dc.format.extent | 19 | |
dc.format.extent | 303761 | |
dc.language.iso | eng | |
dc.relation.ispartof | Israel Journal of Mathematics | en |
dc.subject | Presented simple-groupsS | en |
dc.subject | Finiteness properties | en |
dc.subject | Local similarities | en |
dc.subject | Automata groups | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Some isomorphism results for Thompson-like groups Vn(G) | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1007/s11856-017-1580-5 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2018-11-08 |
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