GAG 2019

Multilinear tools through filters on groups 

 

​

We introduce filters for nilpotent groups to uncover structure using tools from multilinear and nonassociative algebra. We focus in particular on two main themes: studying local properties through bilinear maps, and studying global structure on graded Lie algebras. Even in the extreme case where the only classically known characteristic subgroup is the commutator, these methods can produce maximal characteristic series. We discuss applications to isomorphism testing of groups. We report on individual and joint work with Peter A. Brooksbank, Uriya First, and James B. Wilson.