期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/281734
出版社：Hindawi Publishing Corporation
摘要：The commutator length “cl(𝐺)” of a group 𝐺 is the least natural number 𝑐 such that every element of the derived subgroup of 𝐺 is a product of 𝑐 commutators. We give an upper bound for cl(𝐺) when 𝐺 is a 𝑑-generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over 𝐂 that depends only on 𝑑 and the degree of linearity. For such a group 𝐺, we prove that cl(𝐺) is less than
𝑘(𝑘
