Methods for Investigating Finitely-presented Groups
Author | : Matthew Auger |
Publisher | : |
Total Pages | : 88 |
Release | : 2011 |
ISBN-10 | : OCLC:746125871 |
ISBN-13 | : |
Rating | : 4/5 (71 Downloads) |
Book excerpt: 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.