Model theoretic advances for groups with bounded chains of centralizers

Model theory seminarCUNY Logic WorkshopFriday, March 28, 201412:30 pm

Paul Baginski

Model theoretic advances for groups with bounded chains of centralizers

Fairfield University

Stable groups have a rich literature, extending ideas about algebraic groups to a wider setting, using the framework of model theory. Stable groups gain much of their strength through their chain conditions, notably the Baldwin-Saxl chain condition. In this talk, we will concern ourselves with one mild, yet very important, chain condition shared by many infinite groups studied by group theorists. A group $G$ is said to be $M_C$ if every chain of centralizers $C_G(A_1)$ ≤ $C_G(A_2)$ ≤ ⋅ ⋅ ⋅ is finite. This class is not elementary, yet there is increasing evidence that they share many important properties of stable groups. All the present results concern nilpotence in $M_C$ groups. The first results in this area were purely group-theoretic, but recent results by Wagner, Altinel and Baginski have uncovered that some of the desired definability results are also present. We will recount the progress that has been made and the obstacles that researchers in this area face.

This joint meeting of the Model Theory Seminar and the CUNY Logic Workshop will take place at 12:30 pm, the usual Model Theory time.
Posted by on March 5th, 2014