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
Famous quotes containing the words ends and/or groups:
“One who is publicly honest about himself ends up by priding himself somewhat on this honesty: for he knows only too well why he is honestfor the same reasons another person prefers illusion and dissimulation.”
—Friedrich Nietzsche (18441900)
“Some of the greatest and most lasting effects of genuine oratory have gone forth from secluded lecture desks into the hearts of quiet groups of students.”
—Woodrow Wilson (18561924)