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Amenable actions of nonamenable groups

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Abstract

We present two methods of constructing amenable (in the sense of Greenleaf) actions of nonamenable groups. In the first part of the paper, we construct a class of faithful transitive amenable actions of the free group using Schreier graphs. In the second part, we show that every finitely generated residually finite group can be embedded into a bigger residually finite group, which acts level-transitively on a locally finite rooted tree, so that the induced action on the boundary of the tree is amenable on every orbit. Bibliography: 25 titles.

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Authors and Affiliations

  1. Texas A&M University, USA

    R. Grigorchuk & V. Nekrashevych

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  1. R. Grigorchuk
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  2. V. Nekrashevych
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 85–96.

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Grigorchuk, R., Nekrashevych, V. Amenable actions of nonamenable groups. J Math Sci 140, 391–397 (2007). https://doi.org/10.1007/s10958-007-0448-z

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