In this project we study varieties V(w) defined by single elements
w of the free group F2. The goal of the project would
discover when V(wi) is contained in V(wj), or equivalently, when the identity wi implies on the identity wj. (For example,
groups of exponent 2 are commutative, so the identity x2 implies the identity [x,y] := x-1 y-1 xy.) If wi does not imply wj then
we try to produce an example of a group G in V(wi) that is not in V(wj), where G is small in some sense.
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.