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

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6327)

Abstract

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.

Keywords

  • Polycyclic quotient
  • nilpotent quotient
  • finitely presented group
  • L-presented group
  • Groebner bases

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Eick, B., Horn, M. (2010). Computing Polycyclic Quotients of Finitely (L-)Presented Groups via Groebner Bases. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-15582-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)