14 research outputs found
Almost simple groups as flag-transitive automorphism groups of 2-designs with {\lambda} = 2
In this article, we study -designs with admitting a
flag-transitive almost simple automorphism group with socle a finite simple
exceptional group of Lie type, and we prove that such a -design does not
exist. In conclusion, we present a classification of -designs with
admitting flag-transitive and point-primitive automorphism groups
of almost simple type, which states that such a -design belongs to an
infinite family of -designs with parameter set and
for some , or it is isomorphic to the -design with
parameter set , , , , ,
, , , or
Alternating groups as flag-transitive automorphism groups of 2-designs with block size seven
In this article, we study flag-transitive - designs with
small block size. We show that if is prime, then is point-primitive. In
particular, we show that if , then is of almost simple or affine type.
We also prove that if is a -design with admitting
flag-transitive almost simple automorphism group with socle an alternating
group, then is with parameter set and
, or is the -design with parameter set
and or