Cayley Graphs and Thompson's Group

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Cayley Graphs Cayley graphs are geometric objects used to study finitely generated groups. Let G be a group and let S be a finite generating set for G. Then the associated Cayley graph Γ have vertices associated to the elements of G and (directed) edges corresponding to right multiplication by the elements of S. (12) (12) e e (132) (123) (132) (123) (23) (13) (23) (13) 2
Dihedral Groups Dihedral groups are generated by a reflection and a (minimal, non-trivial) rotation. The associated Cayley graph for D 4 is: This highlights that Cayley graphs often illuminate the geometry underpinning a group. 3
Page 1: Cayley Graphs and Thompson’s Grou
Page 5 and 6: Infinite Groups While the main ques
Page 7 and 8: Geometric Questions Many questions
Page 9 and 10: Thompson’s Group Thompson’s gro
Page 11: Strange Facts ... So F ⊕ F < F !

Cayley Graphs and Thompson's Group

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