Finite quasiprimitive permutation groups with a metacyclic transitive subgroup

Finite Transitive Permutation Groups and Finite Vertex-Transitive Graphs

The theory of vertex-transitive graphs has developed in parallel with the theory of transitive permutation groups. In this chapter we explore some of the ways the two theories have influenced each other. On the one hand each finite transitive permutation group corresponds to several vertex-transitive graphs, namely the generalised orbital graphs which we shall discuss below. On the other hand, ...

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

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 lines of the O'NanScott Theorem for finite primitive permutation groups. It is shown that every finite, non-bipartite, 2-arc transitive graph is a cover of a quasiprimitive 2-arc transitive graph. The str...

On Transitive Permutation Groups

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Generating Transitive Permutation Groups