Abstract

The family of multi-EGS groups form a natural generalisation of the Grigorchuk-Gupta-Sidki groups, which in turn are well-studied groups acting on rooted trees. Groups acting on rooted trees provided the first explicit examples of infinite finitely generated torsion groups, and since then have established themselves as important infinite groups, with numerous applications within group theory and beyond. Among these groups with the most interesting properties are the so-called regular branch groups. In this talk we investigate the normal subgroups in non-torsion regular branch multi-EGS groups, and we show that the congruence completion of these multi-EGS groups have bounded finite central width. In particular, we prove that the profinite completion of a Fabrykowski-Gupta group has width 2. This is joint work with Benjamin Klopsch.