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Semi-direct product in groups and Zig-zag product in graphs
 

Summary: Semi-direct product in groups and
Zig-zag product in graphs:
Connections and applications
EXTENDED ABSTRACT
Noga Alon
Alexander Lubotzky
Avi Wigderson
.
Abstract
We consider the standard semi-direct 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 constant-degree
expanding Cayley graphs from small ones.
In [LW93], Lubotzky and Weiss asked whether expan-
sion is a group property; namely, is being expander for

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics