EVENT DETAILS AND ABSTRACT

Title: Identities, probabilistic identities, and approximate identities in group theory
Speaker: Michael Larsen
Speaker Info: Indiana University
Brief Description:
Special Note:
Abstract:

An identity for a group G is a word w in some free group F which yields the identity element whenever elements of G are substituted for the generators of F in w. There are interesting theorems (of which the Tits Alternative is the prototype) which say that a group which satisfies a non-trivial identity does so for a trivial reason; for instance, every abelian group satisfies the identity xyx^{-1}y^{-1}. I will discuss this and then consider what happens when the notion of identity is weakened.