Polynomials describing the multiplication in finitely generated torsion-free nilpotent groups. (May 2019)

• Record Type: Journal Article
• Authors: Cant, Alexander; Eick, Bettina
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 203
• Page End: 210
• Publication Date: 2019-05
• Subjects: Torsion-free nilpotent groups -- Algebraic computation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.04.014
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A famous result of Hall asserts that the multiplication and exponentiation in finitely generated torsion-free nilpotent groups can be described by rational polynomials. We describe an algorithm to determine such polynomials for all torsion-free nilpotent groups of given Hirsch length. We apply this to determine the Hall polynomials for all such groups of Hirsch length at most 7.