Homogeneous actions on the Random Graph

Abstract : We show that any free product of two (non-trivial) countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend our results to groups acting on trees. Finally, we show the ubiquity of finitely generated free dense subgroups of the automorphism group of the Random Graph whose action on it have all orbits infinite .
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01902444
Contributeur : Yves Stalder <>
Soumis le : mardi 23 octobre 2018 - 15:25:49
Dernière modification le : vendredi 14 décembre 2018 - 09:37:39

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  • HAL Id : hal-01902444, version 1

Citation

Pierre Fima, Soyoung Moon, Yves Stalder. Homogeneous actions on the Random Graph. 2018. 〈hal-01902444〉

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