  A finite subset $A$ of an abelian group $G$ is said to be zero-free if the
identity element of $G$ cannot be written as a sum of distinct elements from
$A$. In this article we study the structure of zero-free subsets of $Z/pZ$ the
cardinality of which is close to largest possible. In particular, we determine
the cardinality of the largest zero-free subset of $Z/pZ$, when $p$ is a
sufficiently large prime.
