International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 74981, 9 pages
On the commutator lengths of certain classes of finitely
1Mathematics Department, Teacher Training University, 49 Mofateh Avenue, Tehran 15614, Iran
2Institute of Mathematics, St. Andrews University, St. Andrews, Scotland KY16 9SS, UK
Received 23 June 2004; Revised 4 July 2005; Accepted 28 March 2006
Copyright © 2006 H. Doostie and P. P. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For a finite group , the least
positive integer is called the maximum length of
with respect to the generating set if every element of may
be represented as a product of at most elements of .
The maximum length of , denoted by , is defined to be
the minimum of . The well-known commutator length of a group
, denoted by , satisfies the inequality , where is the derived subgroup of . In this paper
we study the properties of and by using this inequality
we give upper bounds for the commutator lengths of certain classes
of finite groups. In some cases these upper bounds involve the
interesting sequences of Fibonacci and Lucas numbers.