Groups defined by language theoretic classes

Abstract

In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups. We show this class is closed under taking direct products and standard restricted wreath products with virtually free top groups. We also show the class is closed under passing to finite index overgroups and finitely generated subgroups. Further, we show that this class contains the free product Zn * Zm as well as Zn * G for any virtually free group G.

The second topic that we consider is a new class of groups that we introduce called epiregular groups. We show that this class contains all automatic groups and the Baumslag-Solitar group BS(1,2). Further we show that the class of epiregular groups is closed under taking graph products, and passing to finite index overgroups.