33 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
On groups with the same character degrees as almost simple groups with socle the Mathieu groups
Let be a finite group and denote the set of complex irreducible
character degrees of . In this paper, we prove that if is a finite group
and is an almost simple group whose socle is Mathieu group such that , then there exists an Abelian subgroup of such that is
isomorphic to . This study is heading towards the study of an extension of
Huppert's conjecture (2000) for almost simple groups.Comment: arXiv admin note: text overlap with arXiv:1108.0010 by other author
Sporadic simple groups as flag-transitive automorphism groups of symmetric designs
In this article, we study symmetric designs admitting flag-transitive,
point-imprimitive almost simple automorphism groups with socle sporadic simple
groups. As a corollary, we present a classification of symmetric designs
admitting flag-transitive automorphism group whose socle is a sporadic simple
group, and in conclusion, there are exactly seven such designs, one of which
admits a point-imprimitive automorphism group and the remaining are
point-primitive