Class of intersection numbers of a homomorphic image in the study of difference sets with order 49

Abstract

The investigation of (v,k,λ) difference sets involves the computation of intersection numbers of homomorphic images of the underlying group. Up to compliments, there are fifteen difference set parameters with order 49 but only three of these parameter sets, namely, (400, 57, 8), (280, 63, 14) and (220, 73, 24) satisfy v ≡ 0 mod 20. In this paper, we demonstrate how to construct difference set images for these parameter sets in Frobenius group of order 20, Frob(20). We also conclude that if Gis a group of order 220 with factor group H that is isomorphic to Frob(20) then Gdoes not admit (220, 73, 24) difference sets.

Keywords: Difference sets, symmetric designs, affine plane, representations and groups

Journal of the Nigerian Association of Mathematical Physics, Volume 15 (November, 2009), pp 13 - 26