  Let $N$ and $H$ be groups, and let $G$ be an extension of $H$ by $N$. In this
article we describe the structure of the complex group ring of $G$ in terms of
data associated with $N$ and $H$. In particular, we present conditions on the
building blocks $N$ and $H$ guaranteeing that $G$ satisfies the zero-divisor
and idempotent conjectures. Moreover, for central extensions involving amenable
groups we present conditions on the building blocks guaranteeing that the
Kadison-Kaplansky conjecture holds for the group C*-algebra of $G$.
