 
Summary: Semidirect product in groups and
Zigzag product in graphs:
Connections and applications
EXTENDED ABSTRACT
Noga Alon
Alexander Lubotzky
Avi Wigderson
.
Abstract
We consider the standard semidirect product A B
of finite groups A, B. We show that with certain choices
of generators for these three groups, the Cayley graph of
A B is (essentially) the zigzag product of the Cayley
graphs of A and B. Thus, using the results of [RVW00],
the new Cayley graph is an expander if and only if its
two components are. We develop some general ways of
using this construction to obtain large constantdegree
expanding Cayley graphs from small ones.
In [LW93], Lubotzky and Weiss asked whether expan
sion is a group property; namely, is being expander for
