We plan to study universal linear pro-p groups, that is pro-p groups generated by generic matrices. The aim is to use recent advances in the theory of PI-algebras to show that certain relative verbal widths are finite. This will imply that free pro-p groups, and hence Golod-Shafarevich groups, are not linear.
The expected results will affect several branches of Algebra and shed light on infinite algebraic objects that feature quite prominently in Algebraic Number Theory. The PI intends to involve three graduate students that he currently advises in the work on the project.
