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Vertex stabilizers of graphs and tracks, I
- Source :
-
European Journal of Combinatorics . Feb2007, Vol. 28 Issue 2, p613-640. 28p. - Publication Year :
- 2007
-
Abstract
- Abstract: This paper is devoted to the conjecture saying that, for any connected locally finite graph and any vertex-transitive group of automorphisms of , at least one of the following assertions holds: (1) There exists an imprimitivity system of on with finite (maybe one-element) blocks such that the stabilizer of a vertex of the factor graph in the induced group of automorphisms is finite. (2) The graph is hyperbolic (i.e., for some positive integer , the graph defined by and contains the regular tree of valency 3). Our approach to the conjecture consists in fixing a finite permutation group and considering the conjecture under the assumption that the stabilizer of a vertex of in induces on the neighborhood of the vertex a group permutation isomorphic to . In the paper we elaborate a method (the modified track method) which allows us to prove the conjecture for many groups . The paper consists of two parts. The present first part of the paper involves results on which the modified track method arguments are based, and a few first applications of the method. The second part is devoted to applications of the modified track method. [Copyright &y& Elsevier]
- Subjects :
- *GROUP theory
*ALGEBRA
*SET theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 28
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 23229313
- Full Text :
- https://doi.org/10.1016/j.ejc.2005.05.010