## Generic subsets of Thompson's group

- Date: 11/21/2006

Murray Elder (Stevens Institute of Technology)

University of British Columbia

Richard Thompson constructed an example of a group which is called

'F'that has many unusual properties. One way to consider its elements

is in terms of pairs of rooted binary trees. This viewpoint lends

itself nicely to counting subsets of elements with particular

properties. Meanwhile in cryptography, interest turned to finding

algebraic structures (like groups) on which to base cryptosystems.

These groups should have problems or properties that are hard to decide

(in some sense). A property of a group or set is 'generic' if one can

place a probabilistic measure on elements so that the subset of

elements enjoying the property has measure 1. So in an effort to make

sense of this we try it out on Thompson's group F - we define a measure

and look for properties of the group, or subgroups of the group, that

are in this sense 'generic'.

This is joint work with Jennifer Taback, Bowdoin, Maine, and should be accessible to all.

Discrete Math Seminar 2006