The efficiency on 2-generators of semi-direct product of groups

Authors : A. S. ÇEVİK

Pages : 0-0

Doi:10.1501/Commua1_0000000391

View : 5 | Download : 9

Publication Date : 1999-01-01

Article Type : Research Paper

Abstract :Let G be a semi-direct product of K by A where K and A are both cyclic groups of order n insert ignore into journalissuearticles values(n e N); and p insert ignore into journalissuearticles values(p is a prime);, respectively. Then we prove that G has an efficient presentation on the minimal ııumber, that is 2, of generators. After ali, as an application of our main result. we give the efficiency of the dihedral group Dln and the metacylic group of order 2m insert ignore into journalissuearticles values( m > 4 and m iseven);.
Keywords : semi direct, efficiency, product