Combinatorial Designs and Groups

Construction of designs by assuming a certain automorphism group is a powerful method first developed extensively by R. C. Bose. Recently the symmetric designs with v 56, k 11, lambda 2 and v 79, k 13, lambda 2 have been constructed by such methods. Examples of this method, including these two are given in section 2. Section 3 studies groups generated by a class C of elements of order 3 in which any two non-commuting elements generate SL2,3. Here the four groups of order 3 in SL2,3 may be considered a block of 4 points, and the study of such groups may be related to designs with k 4, lambda 1.