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On the dimension of matrix representations of finitely generated torsion free nilpotent groups
-
Maggie Habeeb
and
Delaram Kahrobaei
Published/Copyright:
October 16, 2013
Abstract.
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].
Received: 2011-09-19
Revised: 2013-01-21
Published Online: 2013-10-16
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
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- Another look at non-uniformity
- An asymmetric generalisation of Artin monoids
- Non-associative key establishment for left distributive systems
- On the dimension of matrix representations of finitely generated torsion free nilpotent groups
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Articles in the same Issue
- Masthead
- Another look at non-uniformity
- An asymmetric generalisation of Artin monoids
- Non-associative key establishment for left distributive systems
- On the dimension of matrix representations of finitely generated torsion free nilpotent groups
- On the intersection of subgroups in free groups: Echelon subgroups are inert
- A secret sharing scheme based on the Closest Vector Theorem and a modification to a private key cryptosystem
