p-quotients of the G.Higman group

These notes are based on the mini-course “On the Graham Higman group”, given at the Erwin Schr"odinger Institute in Vienna, January 20, 22, 27 and 29, 2016, as a part of the Measured Group Theory program. The main purpose is to describe p-quotients of the Higman group $H(k)$ for $p\mathrm{\mid }(k-1)$. (One may check that the condition $p\mathrm{\mid }(k-1)$ is necessary for the existence of such quotients.)