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A famous result of Hall asserts that the multiplication and exponentiation infinitely generated torsion free nilpotent groups can be described by rationalpolynomials. We describe an algorithm to determine such polynomials for alltorsion free nilpotent groups of given Hirsch length. We apply this todetermine the Hall polynomials for all such groups of Hirsch length at most 7.

Polynomials describing the multiplication in finitely generated torsion free nilpotent groups