Startseite Mathematik Dense free subgroups of automorphism groups of homogeneous partially ordered sets
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Dense free subgroups of automorphism groups of homogeneous partially ordered sets

  • Szymon Głab ORCID logo , Przemysław Gordinowicz ORCID logo und Filip Strobin EMAIL logo
Veröffentlicht/Copyright: 20. September 2018

Abstract

A countable poset is ultrahomogeneous if every isomorphism between its finite subposets can be extended to an automorphism. If A is such a poset, then the group Aut(A) has a natural topology in which Aut(A) is a Polish topological group. We consider the problem of whether Aut(A) contains a dense free subgroup of two generators. We show that if A is ultrahomogeneous, then Aut(A) contains such a subgroup. Moreover, we characterize those countable ultrahomogeneous posets A such that for each natural number m the set of all cyclically dense elements g¯Aut(A)m for the diagonal action is comeager in Aut(A)m. In our considerations we strongly use the result of Schmerl which says that there are essentially four types of countably infinite ultrahomogeneous posets.


Communicated by Manfred Droste


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Received: 2017-08-01
Revised: 2018-07-20
Published Online: 2018-09-20
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 4.2.2026 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2017-0162/pdf
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