TY - JOUR

T1 - On the commutator lengths of certain classes of finitely presented groups

AU - Doostie, H.

AU - Campbell, P.P.

PY - 2006

Y1 - 2006

N2 - For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G - {1}}. The well-known commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) 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.

AB - For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G - {1}}. The well-known commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) 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.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-33749513941&partnerID=8YFLogxK

U2 - 10.1155/IJMMS/2006/74981

DO - 10.1155/IJMMS/2006/74981

M3 - Article

AN - SCOPUS:33749513941

SN - 0161-1712

VL - 2006

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

M1 - 74981

ER -