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TitleComputing polycyclic quotients of finitely ($L$-)presented groups via Groebner bases.
Author(s) Bettina Eick, Max Horn
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe 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.
KeywordsPolycyclic quotient, nilpotent quotient, finitely presented group, L-presented group, Groebner bases
URL http://link.springer.com/chapter/10.1007%2F978-3-642-15582-6_10
PublisherBerlin: Springer
Translation No
Refereed No