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It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into for an appropriate ; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [J. Algebra 300 (2006), 376–383]. In this paper, we determine the complexity of the crux of the algorithm and the dimension of the matrices produced as well as provide a modification of the algorithm presented in [J. Algebra 300 (2006), 376–383].
Keywords: Nilpotent; dimension; polycyclic
Published Online: 2013-10-16
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston