Applying Gröbner basis techniques to group theory

We apply the machinery of Gröbner bases to finitely presented groups. This allows for computational methods to be developed which prove that a given finitely presented group is not nn-linear over a field kk assuming some mild conditions. We also present an algorithm which determines whether or not a finitely presented group GG is trivial given that an oracle has told us that GG is nn-linear over an algebraically closed field kk.