Groups, ends and trees: exercises II Michele Triestino 2015-07-22 Exercise 1. ... Show that the function dS : G Ґ G - G defined by dS (x, y) = x-1 y S is a distance on G and coincides with the graph distance on the Cayley graph of G with respect to generating set S. Exercise 4. ... Let S and S be two different finite generating sets of a group G. Show that the Cayley graphs (G, S) and (G, S) are quasi-isometric. ... Show that the Cayley graph of a finite group is quasi-isometric to a point. ...

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