Quotients of \'etale groupoids and the abelianizations of groupoid C*-algebras

In this paper, we introduce quotients of 'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an 'etale groupoid is implied by the full uniqueness property of its groupoid C*-algebra.