Presented by Dr. Robert MORSE
Type: Oral presentation
A group $G$ is called capable if there exists a group $H$ such that $H/Z(H)$ is isomorphic to $G$. It was recognised by P. Hall that capability has application in classifying $p$-groups. This application was developed and applied by M. Hall and Senior to classify the groups of order $64$. There are several methods for determining whether a $p$-group is capable. In this talk we will review these methods and describe classes of groups $p$-group for which we have a complete description of those that are capable. Recent and ongoing work in this area includes the $2$-generator $p$-groups of class $2$ and the special $p$-groups of rank $2$.