Computing Polycyclic Quotients of Finitely (L-)Presented Groups via Groebner Bases

摘要

We announce the development and implementation of a new GAP package PCQL. This facilitates the computation of consistent polycyclic presentations for polycyclic quotients of groups denned by a so-called finite L-presentation. This type of presentation incorporates all finite presentations as well as certain infinite presentations. The algorithm allows a variety of polycyclic quotients ranging from maximal nilpotent quotients of a given class to the maximal solvable quotients of a given derived length. The algorithm uses Groebner bases over integral group rings of polycyclic groups as main means of its computation.