22 research outputs found
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
Symmetry properties of subdivision graphs
The subdivision graph of a graph is obtained from
by `adding a vertex' in the middle of every edge of \Si. Various
symmetry properties of are studied. We prove that, for a connected
graph , is locally -arc transitive if and only if
is -arc transitive. The diameter of
is , where has diameter and , and local -distance transitivity of is
defined for . In the general case where
we prove that is locally -distance transitive
if and only if is -arc transitive. For the
remaining values of , namely , we classify
the graphs for which is locally -distance transitive in
the cases, and . The cases remain open
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