Methods For Investigating Finitely Presented Groups

This thesis concerns computation with finite group presentations and its application to resolve certain open problems of Kim and Kostrikin. We use the low-index subgroups and abelian quotient invariants algorithms to show that each member of a certain family of finitely-pesented groups is infinite. We present a new algorithm for determining which generalised dihedral groups are quotients of a given finitely-presented group, and use this to show that the groups in another family are pairwise non-isomorphic. Also we describe the method of 'pictures' over group presentations, discussing what they represent and how they can be used to obtain information about the group.