Reduction for flag‐transitive 2‐(v,k,λ) designs with (r,λ)=2

Abstract

This paper studies flag‐transitive 2‐ ( v , k , λ ) designs with ( r , λ ) = 2. We prove that if MJX-tex-caligraphicscriptD is a flag‐transitive nontrivial 2‐ ( v , k , λ ) design with ( r , λ ) = 2, then G is of affine or almost simple type. Furthermore, we analyze the flag‐transitive automorphism groups of almost simple type with S o c ( G ) = A n for n ≥ 5, and obtain that, up to isomorphism, there are 11 designs.

Block‐transitive automorphism groups of 2‐(v,k,λ) $(v,k,\lambda )$ designs with (r,k)=1 $(r,k)=1$

“…The reductions for flag-transitive automorphism groups of 2-designs with additional conditions r λ ( , ) = 1 or n k ( , ) = 1 have been finished and the rest are under way, see [20][21][22]24]. Theorem 1 actually gives a new condition r k ( , ) = 1 which is different from Dembowski' conditions under the weaker assumptions that G is blocktransitive.…”