On the dimension of matrix representations of finitely generated torsion free nilpotent groups

被引：1
|
作者：
Habeeb, Maggie [1 ]
Kahrobaei, Delaram [2 ,3 ]
机构：
[1] Calif Univ Penn, Dept Math Comp Sci & Informat Syst, Philadelphia, PA 19104 USA
[2] CUNY, CUNY Grad Ctr & City Tech, Dept Comp Sci, New York, NY USA
[3] CUNY, CUNY Grad Ctr & City Tech, Dept Math, New York, NY USA
来源：
GROUPS COMPLEXITY CRYPTOLOGY | 2013年 / 5卷 / 02期
关键词：
Nilpotent; dimension; polycyclic;
D O I：
10.1515/gcc-2013-0011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is well known that any polycyclic group, and hence any finitely generated nilpotent group, can be embedded into GL(n)(Z) for an appropriate n is an element of N; that is, each element in the group has a unique matrix representation. An algorithm to determine this embedding was presented in [6]. 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 [6].
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页码：193 / 209
页数：17
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