Non-commutative super approximation and the product replacement algorithm
Non-commutative super approximation and the product replacement algorithm
Abstract: Let A be the free abelian group on n generators and C a finite simple abelian
group. The action of Aut(A) on E = Epi(A, C) ( = the set of epimorphisms from A to C)
satisfies super-approximation (i.e., the induced graph is an expander). We will discuss the
situation when A is replaced the non-abelian free group F and C a non-abelian finite simple
group S. This question is of interest in presentation theory of finite groups as well as for
analyzing the product replacement algorithm which is an important and useful algorithm in
computational group theory. If time permits we will also discuss the situation when M(g)
(= the mapping class group) replaces Aut(F).
Date
Speakers
Alex Lubotzky
Affiliation
The Hebrew University of Jerusalem