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Эта публикация цитируется в 8 научных статьях (всего в 8 статьях)
Статьи
On the stabilizers of finite sets of numbers in the R. Thompson group $F$
G. Golan, M. Sapir Vanderbilt University, 2201 West End Ave, Nashville, TN 37235, USA
Аннотация:
The subgroups $H_U$ 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 $H_U$ is described and it is proved that the stabilizer $H_U$ 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 $U\subset[0,1]$ and $V\subset[0,1]$ consist of rational numbers that are not finite binary fractions, and $|U|=|V|$, then the stabilizers of $U$ and $V$ are isomorphic. In fact these subgroups are conjugate inside a subgroup $\bar F<\operatorname{Homeo}([0,1])$ 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 $\mathcal F<\bar F$ which consists of possibly infinite tree-diagrams with finitely many infinite branches. It is also shown that the group $\mathcal F$ is non-amenable.
Ключевые слова:
Thompson group $F$, stabilizers.
Поступила в редакцию: 15.05.2016
Образец цитирования:
G. Golan, M. Sapir, “On the stabilizers of finite sets of numbers in the R. Thompson group $F$”, Алгебра и анализ, 29:1 (2017), 70–110; St. Petersburg Math. J., 29:1 (2018), 51–79
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1523 https://www.mathnet.ru/rus/aa/v29/i1/p70
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