Primitive Permutation Groups of Unitary type with a regular Subgroup

Primitive Permutation Groups of Simple Diagonal Type

Let G be a finite primitive group such that there is only one minimal normal subgroup M in G, this M is nonabelian and nonsimple, and a maximal normal subgroup of M is regular. Further, let H be a point stabilizer in G. Then H (1 M is a (nonabelian simple) common complement in M to all the maximal normal subgroups of M, and there is a natural identification ofMwith a direct power T m of a nonab...

Distinguishing Primitive Permutation Groups

Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.

Digraph Representations of 2-closed Permutation Groups with a Normal Regular Cyclic Subgroup

In this paper, we classify 2-closed (in Wielandt’s sense) permutation groups which contain a normal regular cyclic subgroup and prove that for each such group G, there exists a circulant Γ such that Aut(Γ) = G.

Factorizations of Primitive Permutation Groups

Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph Kn , a lexicographic product [K̄b], a deleted lexicographic product [K̄b] − b , where ...