International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 821-824

On mennicke groups of deficiency zero I

Muhammad A. Albar

Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi Arabia

Received 26 March 1985; Revised 20 May 1985

Copyright © 1985 Muhammad A. Albar. 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.


The Mennicke group M(m,n,r)=x,y,z,|xy=xm, yz=yn, zx=zr is one of the few known 3-generator groups of deficiency zero. Several cases of M(m,n,r) are studied.