Analytic and Geometric Group Theory At IMPAN

Organized by Mark Pengitore, Antonio López Neumann, and Piotr Nowak

Fridays at 11:00 - 12:30 at Room 106

Next Seminar

08/11/2024, 11:00 -- 12:30

Speaker: Mark Pengitore (IM PAN)

Title: Automorphism groups of solvable groups of finite abelian ranks

Abstract: I will introduce the collection of solvable groups of finite abelian ranks, which is a group of solvable groups that have resisted many geometric techniques that are typically used in group theory.  We will discuss basic examples, properties, and invariants of these groups. We will then introduce the Q-algebraic hull of a solvable group G of finite abelian ranks, which is a linear algebraic group that can be used to model automorphisms of G. As an application of this Q-algebraic hull, we finish by demonstrating that the outer automorphism group of a linear solvable group of finite abelian ranks is S-arithmetic when the Fitting subgroup is S-arithmetic, which is a generalization of a celebrated result of Baues-Grunewald.