Table of Contents
International Journal of Combinatorics
Volume 2010, Article ID 502989, 6 pages
Research Article

Bitranslations and Symmetric Nets

Department of Mathematics, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia

Received 20 November 2009; Accepted 13 April 2010

Academic Editor: Charles Semple

Copyright © 2010 Ahmad N. Al-Kenani. 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.


It is known that every class-regular symmetric ( 𝜇 , 𝑚 ) -net is tactical. Also it is known that all ( 𝜇 , 𝑚 ) -nets with 𝑚 = 2 or 𝜇 = 1 are tactical. In the work of Al-Kenani and Mavron (2003), it is proved that every symmetric net with 𝑚 = 3 is tactical if and only if it is class regular. In this paper, we construct ( 2 , 4 ) -net and show that it is class regular and therefore tactical. New necessary and sufficient conditions are given for a symmetric net to admit a nonidentity bitranslation.