Professor: Sims, Mathematics Department, Rutgers University.

Student: James Otterson, Rutgers University.

Project Description:

In this project we study varieties V(w) defined by single elements
w of the free group F_{2}. The goal of the project would
be to

discover when V(w_{i}) is contained in V(w_{j}), or
equivalently, when the identity w_{i }implies on the identity w_{j}.
(For example,

groups of exponent 2 are commutative, so the identity x^{2
}implies the identity [x,y] := x^{-1} y^{-1} xy.)
If w_{i }does not imply w_{j} then

we try to produce an example of a group G in V(w_{i}) that
is not in V(w_{j}), where G is small in some sense.

References:

Varieties of Groups,
*H. Neumann, Springer Verlag*

Computation with Finetely Presented Groups,
*C. Sims, Cambridge*

A Course in the Theory of Groups, *D. Robinson, GTM Springer
Verlag.*

Algebra, *T. Hungerford, GTM, Springer Verlag*.

So far I have being working in this project with professor Sims for
a year. Some instances of the problem have

being classified. The project will probably continue in the next
semester.