Abstract
Let G be an infinite group and let S be a finite subset of G . The outconnectivity of the Cayley graph X = Cay ( G , S ) is κ + ( X )= Min {|( FS ) z . drule ; F |: F is a finite nonvoid subset of G }. A positive end is a finite subset R such that κ + ( X )=|( RS )⧹ R |, which is minimal with respect to this property. We prove that there is a unique positive end containing 1. Moreover this end is a subgroup. As an application we deduce some properties of the connectivity which were known only in the finite case.
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