In this article, we investigate 2- $$(v,k,\lambda )$$ designs with $$\gcd (r,\lambda )=1$$ admitting flag-transitive automorphism groups G. We prove that if G is an almost simple group, then such a design belongs to one of the eight infinite families 2-designs or it eleven well-known examples. describe all these examples designs. We, in particular, $${\mathcal {D}}$$ symmetric (k,\lambda group ...

Tits [ 191 has initiated the study of geometries having properties strongly resembling those of buildings (compare [6]). His main result is that, in general, such a geometry is the image of a building under a suitable type of morphism. These geometries that are almost buildings were called GABS in [lo], and finite examples were described in [2, 8, 10, 15, 161 that are not buildings but have hig...

This article is a contribution to the study of the automorphism groups of 2−(v, k, 1) designs. Let D be 2−(v, 13, 1) design, G ≤ Aut(D) be block transitive, point primitive but not flag transitive. Then Soc(G), the socle of G, is not classical simple group over finite filed GF (q)(q odd). Mathematics Subject Classification: 05B05, 20B25