In joint work with Brendan Mallery, we introduce and study so called “shift-similar” groups. Self-similar groups are a well known class of groups, which in particular interact nicely with Higman-Thompson groups, and we introduce shift-similar groups as an analog that interacts nicely with Houghton groups. Shift-similar groups actually turn out to have many properties that self-similar groups do not, for example every finitely generated group embeds into some finitely generated shift-similar group, and there exist uncountably many finitely generated shift-similar groups. In this talk I will recall some background on self-similar groups, introduce shift-similar groups and the Houghton-like groups they produce, and discuss the aforementioned results plus some results about amenability. I will also highlight some open questions.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
