Department of Mathematics

A group \( G \) is left-orderable (LO) if there exists a linear ordering of \( G \) that is invariant under multiplication on the left. A left-ordering is Conradian if for any \( g,h >1 \) in \( G \), we have \( g\lt hg^2 \). Nilpotent LO groups admit only Conradian left-orderings, but finding non-nilpotent LO groups that admit only Conradian left-orderings turns out to be non-trivial.

This talk will open with a brief overview of the motivation for finding such groups, then go through the construction of Golod groups and discuss their properties, with an emphasis on the conditions under which Golod groups are non-nilpotent LO groups that admit only Conradian left-orderings.