Uniform simplicity for subgroups of piecewise continuous bijections of the unit interval
نویسندگان
چکیده
Let I = [ 0 , 1 ) $I=[0,1)$ and PC ( $\mathcal {PC}(I)$ (resp. + {PC}^+(I)$ be the quotient group of all piecewise continuous orientation preserving) bijections $I$ by its normal subgroup consisting in elements with finite support (i.e., which are trivial except at possibly finitely many points). Arnoux's thesis states that certain groups interval exchanges simple, proofs these results purpose Appendix. We prove simplicity A {A}^+(I)$ locally preserving, continuous, affine maps unit interval. These can improved. Indeed, a G $G$ is uniformly simple if there exists positive integer N $N$ such for any f ϕ ∈ ∖ { Id } $f,\phi \in G\setminus \lbrace \text{\rm Id}\rbrace$ element $\phi$ written as product most conjugates $f$ or − $f^{-1}$ . provide conditions, guarantee simple. As corollaries, we obtain PL S ${\text{\rm PL}}^+ (\mathbb {S}^1)$ {A}(I)$ some Thompson-like included Thompson T $T$
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ژورنال
عنوان ژورنال: Bulletin of The London Mathematical Society
سال: 2023
ISSN: ['1469-2120', '0024-6093']
DOI: https://doi.org/10.1112/blms.12861