منابع مشابه
Crown-free highly arc-transitive digraphs
We construct a family of infinite, non-locally finite highly arc-transitive digraphs which do not have universal reachability relation and which omit special digraphs called ‘crowns’. Moreover, there is no homomorphism from any of our digraphs onto Z. The methods are adapted from [5] and [6].
متن کاملHighly arc transitive digraphs: reachability, topological groups
Let D be a locally finite, connected, 1-arc transitive digraph. It is shown that the reachability relation is not universal in D provided that the stabilizer of an edge satisfies certain conditions which seem to be typical for highly arc transitive digraphs. As an implication, the reachability relation cannot be universal in highly arc transitive digraphs with prime inor out-degree. Two differe...
متن کاملAn Infinite Highly Arc-transitive Digraph
The main purpose of this note is to construct an infinite , highly arc-transitive digraph with finite out-valency , and with out-spread greater than 1 , which does not have the two-way infinite path Z as a homomorphic image . This answers Question 3 . 8 in the paper [3] of Cameron , Praeger and Wormald . Our digraph has infinite in-valency . By a result of Praeger (see [5]) , a connected , vert...
متن کاملHIGHLY TRANSITIVE ACTIONS OF Out(Fn)
An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≥ 4 the group Out(Fn) = Aut(Fn)/ Inn(Fn) admits a faithful highly transitive action on a countable set.
متن کاملHighly arc-transitive digraphs - Structure and counterexamples
Two problems of Cameron, Praeger, and Wormald [Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica (1993)] are resolved. First, locally finite highly arc-transitive digraphs with universal reachability relation are presented. Second, constructions of two-ended highly arc-transitive digraphs are provided, where each ‘building block’ is a finite bipartite digrap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.11.031