## Abstract

Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact non-compact group this is a nonmetrizable system with a very rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizahle space and for which one has an explicit description. One such group is the topological group S of all the permutations of the integers Z, with the topology of pointwise convergence. In this paper we show that (M(S), S) is a symbolic dynamical system (hence in particular M(S) is a Cantor set), and we give a full description of all its symbolic factors.

Original language | English |
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Pages (from-to) | 964-988 |

Number of pages | 25 |

Journal | Geometric and Functional Analysis |

Volume | 12 |

Issue number | 5 |

DOIs | |

State | Published - 2002 |