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].

引用

页码：193 / 209

页数：17

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