Computing polycyclic quotients of finitely (L-)presented groups via Groebner bases. 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 defined 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.
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- Eick, Bettina; Horn, Max: Computing polycyclic quotients of finitely ($L$-)presented groups via Groebner bases. (2010)