Dead End Words in Lamplighter Groups and Other Wreath Products Sean Cleary and Jennifer Taback
نویسنده
چکیده
We explore the geometry of the Cayley graphs of the lamplighter groups and a wide range of wreath products. We show that these groups have dead end elements of arbitrary depth with respect to their natural generating sets. An element w in a group G with finite generating set X is a dead end element if no geodesic ray from the identity to w in the Cayley graph Γ(G, X) can be extended past w. Additionally, we describe some nonconvex behavior of paths between elements in these Cayley graphs and seesaw words, which are potential obstructions to these graphs satisfying the kfellow traveller property.
منابع مشابه
Metric Properties of the Lamplighter Group as an Automata Group Sean Cleary and Jennifer Taback
We develop the geometry of the Cayley graph of the lamplighter group with respect to the generating set rising from its interpretation as an automata group [4]. We find metric behavior with respect to this generating set analogous to the metric behavior in the standard group theoretic generating set. This includes expressions for normal forms and geodesic paths, and families of ‘dead-end’ words...
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