Smith, Simon (2007) Orbital digraphs of infinite primitive permutation groups. Journal of Group Theory, 10 (6). ISSN 14335883
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
If G is a group acting on a set Ω, and α, β ∈ Ω, the digraph whose vertex set is Ω and whose arc set is the orbit (α, β)G is called an orbital digraph of G. Each orbit of the stabilizer G α acting on Ω is called a suborbit of G.
A digraph is locally finite if each vertex is adjacent to at most finitely many other vertices. A locally finite digraph Γ has more than one end if there exists a finite set of vertices X such that the induced digraph Γ\X contains at least two infinite connected components; if there exists such a set containing precisely one element, then Γ has connectivity one.
In this paper we show that if G is a primitive permutation group whose suborbits are all finite, possessing an orbital digraph with more than one end, then G has a primitive connectivityone orbital digraph, and this digraph is essentially unique. Such digraphs resemble trees in many respects, and have been fully characterized in a previous paper by the author.
Keywords:  Infinite permutation groups, Orbital graphs 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
ID Code:  27495 
Deposited On:  12 May 2017 10:08 
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