On normalish subgroups of the R. Thompson groups
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Results 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.
Bleak , 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 , United States , 11/05/20 . https://doi.org/10.1007/978-3-030-48516-0_3conference
Developments in Language Theory
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DescriptionFunding: UK EPSRC grant EP/R032866/1
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