Polynomials describing the multiplication in finitely generated torsion\n free nilpotent groups

2018/01/09 by A. Cant, Bettina Eick, Cant, Alexander +1
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1801.02932

openalex publication_date 2018/01/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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

Related

• Hall polynomials for the torsion free groups of Hirsch length at most 5
• R_∞-property for finitely generated torsion-free 2-step nilpotent groups of small Hirsch length
• Nilpotent groups with balanced presentations
• Arithmetic Representation Growth of Virtually Free Groups
• Waring's Problem For Locally Nilpotent Groups: The Case of Discrete Heisenberg Groups