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dc.contributor.authorBleak, Collin Patrick
dc.contributor.editorJonoska, Nataša
dc.contributor.editorSavchuk, Dmytro
dc.identifier.citationBleak , C P 2020 , On normalish subgroups of the R. Thompson groups . in N Jonoska & D Savchuk (eds) , Developments in Language Theory : 24th International Conference, DLT 2020, Tampa, FL, USA, May 11–15, 2020, Proceedings . Lecture Notes in Computer Science , vol. 12086 , Springer , pp. 29-42 , 24th International Conference on Developments in Language Theory (DLT) , Tampa , Florida , United States , 11/05/20 .
dc.identifier.otherPURE: 268029453
dc.identifier.otherPURE UUID: 19aef1e5-1239-4a18-b54b-e20940016d6f
dc.identifier.otherScopus: 85086183051
dc.identifier.otherORCID: /0000-0001-5790-1940/work/75248614
dc.identifier.otherScopus: 85086183051
dc.identifier.otherWOS: 000905606300003
dc.descriptionFunding: UK EPSRC grant EP/R032866/1en
dc.description.abstractResults in C∗ algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups F ≤ T ≤ V. These results together show that F is non-amenable if and only if T has a simple reduced C∗-algebra. In further investigations into the structure of C∗-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group G. They show that if a group G admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced C∗-algebra. Our chief result concerns the R. Thompson groups F < T < V; we show that there is an elementary amenable group E < F (where here, E ≅ ...)≀Z)≀Z)≀Z) with E normalish in V. The proof given uses a natural partial action of the group V on a regular language determined by a synchronizing automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of V with various forms of formal language theory.
dc.relation.ispartofDevelopments in Language Theoryen
dc.relation.ispartofseriesLecture Notes in Computer Scienceen
dc.rights© Springer Nature Switzerland AG 2020. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectThompson's groupen
dc.subjectRegular languageen
dc.subjectSynchronizing automataen
dc.subjectGroup actionsen
dc.subjectNormalish sub-groupsen
dc.subjectWreath producten
dc.subjectQA75 Electronic computers. Computer scienceen
dc.subjectTheoretical Computer Scienceen
dc.subjectComputer Science(all)en
dc.titleOn normalish subgroups of the R. Thompson groupsen
dc.typeConference itemen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen

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