Mathematics – Group Theory
Scientific paper
2006-11-24
Mathematics
Group Theory
20B15, 05C25
Scientific paper
10.1515/JGT.2007.060
If $G$ is a group acting on a set $\Omega$ and $\alpha, \beta \in \Omega$, the digraph whose vertex set is $\Omega$ and whose arc set is the orbit $(\alpha, \beta)^G$ is called an {\em orbital digraph} of $G$. Each orbit of the stabiliser $G_\alpha$ acting on $\Omega$ is called a {\it suborbit} of $G$. A digraph is {\em locally finite} if each vertex is adjacent to at most finitely many other vertices. A locally finite digraph $\Gamma$ has more than one end if there exists a finite set of vertices $X$ such that the induced digraph $\Gamma \setminus X$ contains at least two infinite connected components; if there exists such a set containing precisely one element, then $\Gamma$ has {\em 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 connectivity-one orbital digraph, and this digraph is essentially unique. Such digraphs resemble trees in many respects, and have been fully characterised in a previous paper by the author.
No associations
LandOfFree
Orbital graphs of infinite primitive permutation groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Orbital graphs of infinite primitive permutation groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbital graphs of infinite primitive permutation groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-540337