Ambiguous Groups and Cayley Graphs
Arthur Cayley used directed graphs to give a visual representation of the structure of a group. Since then Cayley graphs with undirected edges have been studied by graph theorists as interesting objects in their own right. Without direction on the arrows, a lot of information about the structure of the underlying group is lost- in fact a single Cayley graph may represent two different and non-isomorphic groups.
What happens if we have all possible Cayley graphs for a given group? What does the geometric information tell us about the group? Can we reconstruct the multiplication table of the group? Can we determine the isomorphism class of the group?
The talk, based on joint work with R. Goldstone and J. McCabe, will be accessible to students who have had a modest exposure to abstract algebra.
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