The random graph has the strong small index property
نویسنده
چکیده
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.
منابع مشابه
The small index property for ω-stable ω-categorical structures and for the random graph
We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any ω-stable ω-categorical structure, and (ii) the random graph has the small index property. We also show that the automorphism group of such a structure is not the union of a countable chain of proper subgroups.
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عنوان ژورنال:
- Discrete Mathematics
دوره 291 شماره
صفحات -
تاریخ انتشار 2005