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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Topological dynamics and group theory


Author: Shmuel Glasner
Journal: Trans. Amer. Math. Soc. 187 (1974), 327-334
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1974-0336723-1
MathSciNet review: 0336723
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Abstract: We prove, using notions and techniques of topological dynamics, that a nonamenable group contains a finitely-generated subgroup of exponential growth. We also show that a group which belongs to a certain class, defined by means of topological dynamical properties, always contains a free subgroup on two generators.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0336723-1
Article copyright: © Copyright 1974 American Mathematical Society