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An O'Nan‐Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2‐Arc Transitive Graphs
A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along the linesExpand
Linear Groups with Orders Having Certain Large Prime Divisors
In this paper we obtain a classification of those subgroups of the finite general linear group GLd (q) with orders divisible by a primitive prime divisor of qe − 1 for some . In the course of theExpand
On the O'Nan-Scott theorem for finite primitive permutation groups
We give a self-contained proof of the O'Nan-Scott Theorem for finite primitive permutation groups.
A classification of the maximal subgroups of the finite alternating and symmetric groups
Following the classification of finite simple groups, one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups-that is, ofExpand
Infinite highly arc transitive digraphs and universal covering digraphs
A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs≥0. Expand
On generalised Paley graphs and their automorphism groups
The generalised Paley graphs are, as their name suggests, a generalisation of the Paley graphs, first defined by Paley in 1933 (see \cite{Paley}). They arise as the relation graphs of symmetricExpand
On the orders of Primitive Permutation Groups
CHERYL E. PRAEGE R AN JAD N SAXLThe proble omf bounding the order of a permutation grou G ipn terms of itsdegree n was one of the central problem of 19tsh century group theory (see [4]) It.is closelyExpand
On Finite Affine 2-Arc Transitive Graphs
A 2-arc in a graph ? is a sequence (?, s, ?) of three vertices of ? such that {?, s} and {s, ?} are edges of ?. A graph is said to be affine if there is a vector space N, and a subgroup G of the automorphism group of ?, such that N acting regularly on the vertex set of ? and G acting2-arc-transitively on ?. Expand
Finite normal edge-transitive Cayley graphs