On the Dimension of Matrix Representations of Finitely Generated Torsion Free Nilpotent Groups
Abstract
It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into GLn(Z) for an appropriate n∈ N; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in Nickel. 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 by Nickel.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.