有限生成无扭转幂零群的矩阵表示的维数

Groups Complex. Cryptol. Pub Date : 2013-09-17 DOI:10.1515/gcc-2013-0011

Maggie E. Habeeb, Delaram Kahrobaei

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引用次数: 3

摘要

摘要众所周知，任何多环群，也就是任何有限生成的幂零群，都可以嵌入到一个合适的;也就是说，组中的每个元素都有一个唯一的矩阵表示。一种确定这种嵌入的算法在[J]。代数300(2006)，376-383。在本文中，我们确定了算法关键部分的复杂度和生成矩阵的维数，并对[J]中提出的算法进行了修改。代数300(2006)，376-383。

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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 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].

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Groups Complex. Cryptol.

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