The random graph has the strong small index property

Peter J. Cameron

doi:10.1016/j.disc.2004.04.018

The random graph has the strong small index property

Peter J. Cameron^*

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

Hodges et al. showed that the countable random graph has the small index property. The stronger result of the title is deduced from this and a general theorem about permutation groups. A consequence is that the automorphism group of the random graph is not isomorphic to the automorphism group of any other countable homogeneous graph or digraph.

Original language	English
Pages (from-to)	41-43
Number of pages	3
Journal	Discrete Mathematics
Volume	291
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.04.018
Publication status	Published - 6 Mar 2005

Keywords

Automorphism group
Random graph
Small index property

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10.1016/j.disc.2004.04.018

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abstract = "Hodges et al. showed that the countable random graph has the small index property. The stronger result of the title is deduced from this and a general theorem about permutation groups. A consequence is that the automorphism group of the random graph is not isomorphic to the automorphism group of any other countable homogeneous graph or digraph.",

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AB - Hodges et al. showed that the countable random graph has the small index property. The stronger result of the title is deduced from this and a general theorem about permutation groups. A consequence is that the automorphism group of the random graph is not isomorphic to the automorphism group of any other countable homogeneous graph or digraph.

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JO - Discrete Mathematics

JF - Discrete Mathematics

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The random graph has the strong small index property

Abstract

Keywords

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