Name
Abstract | ||
|---|---|---|
In the first part of this paper we consider nilpotent groups G acting with finitely many orbits on infinite connected locally finite graphs X thereby showing that all α ϵ G of infinite order are automorphisms of type 2 of X . In the second part we investigate the automorphism groups of connected locally finite transitive graphs X with polynomial growth thereby showing that AUT( X ) is countable if and only if it is finitely generated and nilpotent-by-finite. In this case we also prove that X is contractible to a Cayley graph C ( G , H ) of a nilpotent group G (for some finite generating set H ) which has the same growth degree as X . If X is a transitive strip we show that AUT( X ) is uncountable if and only if it contains a finitely generated metabelian subgroup with exponential growth. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1016/0012-365X(91)90120-Q | Discrete Mathematics |
Keywords | Field | DocType |
polynomial growth | Stallings theorem about ends of groups,Discrete mathematics,Combinatorics,Uncountable set,Nilpotent group,Generating set of a group,Automorphism,Cayley graph,Contractible space,Mathematics,Nilpotent | Journal |
Volume | Issue | ISSN |
89 | 3 | Discrete Mathematics |
Citations | PageRank | References |
5 | 1.10 | 3 |
Authors | ||
1 | ||