Ends of Groups
Let G be a finitely generated group. Let S ⊆ G be a finite generating set of G and let Γ(G, S) be the Cayley graph of G with respect to S. The number of ends of G is defined as e(G) = e(Γ(G, S)). A basic fact in the theory of ends of groups says that e(Γ(G, S)) does not depend on the choice of a finite generating set S of G, so that e(G) is well-defined.
Read more about this topic: Stallings Theorem About Ends Of Groups
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