International Journal of Combinatorics
Volume 2011 (2011), Article ID 137356, 12 pages
http://dx.doi.org/10.1155/2011/137356
Research Article

On Some Combinatorial Structures Constructed from the Groups 𝐿 ( 3 , 5 ) , 𝑈 ( 5 , 2 ) , and 𝑆 ( 6 , 2 )

Dean Crnković and Vedrana Mikulić Crnković

Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia

Received 13 January 2011; Revised 30 March 2011; Accepted 26 May 2011

Academic Editor: Christos Koukouvinos

Copyright © 2011 Dean Crnković and Vedrana Mikulić Crnković. 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.

Abstract

We describe a construction of primitive 2-designs and strongly regular graphs from the simple groups 𝐿 ( 3 , 5 ) , 𝑈 ( 5 , 2 ) , and 𝑆 ( 6 , 2 ) . The designs and the graphs are constructed by defining incidence structures on conjugacy classes of maximal subgroups of 𝐿 ( 3 , 5 ) , 𝑈 ( 5 , 2 ) , and 𝑆 ( 6 , 2 ) . In addition, from the group 𝑆 ( 6 , 2 ) , we construct 2-designs with parameters ( 2 8 , 4 , 4 ) and ( 2 8 , 4 , 1 ) having the full automorphism group isomorphic to 𝑈 ( 3 , 3 ) ∶ 𝑍 2 .