A classification of the flag-transitive 2-(v,k,2) designs.

In this paper, we provide a complete classification of 2- (v , k , 2) designs admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear 1-dimensional group. Alongside this analysis, we provide a construction of seven new families of such flag-transitive 2-designs, one of them infinite, and some of them involving remarkable objects such as t -spreads, translation planes, quadrics and Segre varieties. Our result together with those of Alavi et al. [1,2] , Praeger et al. [17] , Zhou and the first author [39,40] provides a complete classification of 2- (v , k , 2) design admitting a flag-transitive automorphism group with the only exception of the semilinear 1-dimensional case. [ABSTRACT FROM AUTHOR]