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Статья «ON THE STABILIZERS OF FINITE SETS OF NUMBERS IN THE R. THOMPSON GROUP F, "Алгебра и анализ"»

Авторы:
  • GOLAN G.1
  • SAPIR M.2
стр. 70-109
Платно
1 Vanderbilt University, 2 Vanderbilt University
  • SDI: 007.001.0234-0852.2017.029.001.5
Аннотация:
The subgroups Hu of the R. Thompson group F that are stabilizers of finite sets U of numbers in the interval (0,1) are studied. The algebraic structure of Hu is described and it is proved that the stabilizer Hu is finitely generated if and only if U consists of rational numbers. It is also shown that such subgroups are isomorphic surprisingly often. In particular, if finite sets U C [0,1] and V C [0,1] consist of rational numbers that are not finite binary fractions, and |t/| = |Vj, then the stabilizers of U and V are isomorphic. In fact these subgroups are conjugate inside a subgroup F < Homeo([0,1]) that is the completion of F with respect to what is called the Hamming metric on F. Moreover the conjugator can be found in a certain subgroup F < F which consists of possibly infinite tree-diagrams with finitely many infinite branches. It is also shown that the group F is non-amenable.

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