Noncommutative Geometry Seminar

Date: November 30, 2017

Time: 2:00PM - 3:00PM

Location: *BLOC 220*

Speaker: Ronghui Ji, IUPUI

Title: From relative amenability to relative soficity for countable groups

Abstract: We define a relative soficity for a countable group with respect to a family of subgroups. A group is sofic if and only if it is relatively sofic with respect to the family consisting of only the trivial subgroup. When a group is relatively amenable with respect to a family of subgroups, then it is relatively sofic with respect to the family. We show that if a group is relatively sofic with respect to a family of sofic subgroups, then the group is sofic. This in particular generalizes a result of Elek and Szabo. An example of relatively amenable group G with respect to an infinite family of subgroups F is constructed so that G is not relatively amenable with respect to any finite subfamily of F.