3-Manifold Seminar: Residual Properties of Groups

Seminar | September 12 | 11:10 a.m.-12:30 p.m. | 939 Evans Hall

 Nic Brody, UC Berkeley

 Department of Mathematics

A group is said to be residually finite if every nontrivial element can be distinguished from the identity in a finite quotient. We introduce the notion of an (alpha, kappa)-residual group, for alpha an ordinal and kappa a cardinal. The ordinal generalization allows one, for example, to measure the degree to which a given group fails to be residually finite in a more refined manner. The cardinal generalization provides a better handle on the space of residual chains in a group. We consider several examples and propose a few questions related to these properties.