  A set of elements of a finite abelian group is called sum-free if it contains
no Schur triple, i.e., no triple of elements $x,y,z$ with $x+y=z$. The study of
how large the largest sum-free subset of a given abelian group is had started
more than thirty years before it was finally resolved by Green and Ruzsa a
decade ago. We address the following more general question. Suppose that a set
$A$ of elements of an abelian group $G$ has cardinality $a$. How many Schur
triples must $A$ contain? Moreover, which sets of $a$ elements of $G$ have the
smallest number of Schur triples? In this paper, we answer these questions for
various groups $G$ and ranges of $a$.
