6 research outputs found
A classification of flag-transitive block designs
In this article, we investigate - designs with
admitting flag-transitive automorphism groups . We prove
that if is an almost simple group, then such a design belongs to one of the
seven infinite families of -designs or it is one of the eleven well-known
examples. We describe all these examples of designs. We, in particular, prove
that if is a symmetric design with
admitting a flag-transitive automorphism group , then
either for some odd prime power , or
is a projective space or the unique Hadamard design with parameters .Comment: arXiv admin note: text overlap with arXiv:1904.1051
Classification of flag-transitive primitive symmetric designs with as socle
Let be a nontrivial symmetric design, and be
a subgroup of the full automorphism group of . In this paper we
prove that if acts flag-transitively, point-primitively on and
, then D has parameters , , , or .Comment: 17 pages, 3 table
Symmetric designs and projective special unitary groups of dimension at most five
In this article, we study symmetric designs admitting a
flag-transitive and point-primitive automorphism group whose socle is a
projective special unitary group of dimension at most five. We, in particular,
determine all such possible parameters and show that there
exist eight non-isomorphic of such designs for which and is , , or
Symmetric designs and four dimensional projective special unitary groups
In this article, we study symmetric designs admitting a
flag-transitive and point-primitive automorphism group whose socle is
. We prove that there exist eight non-isomorphic such designs for
which and is either , or
Flag-transitive non-symmetric -designs with and exceptional groups of Lie type
This paper determined all pairs where is a
non-symmetric 2- design with and is the
almost simple flag-transitive automorphism group of with an
exceptional socle of Lie type. We prove that if
where is an exceptional group of Lie type, then must be the Ree group
or Suzuki group, and there are five classes of non-isomorphic designs
Almost simple groups of Lie type and symmetric designs with prime
In this article, we investigate symmetric designs
with prime admitting flag-transitive and
point-primitive automorphism groups . We prove that if is an almost
simple group with socle a finite simple group of Lie type, then
is either the point-hyperplane design of a projective space
, or it is of parameters , ,
or