Permutation groups, their fundamental theory and applications are discussed in this
introductory book. It focuses on those groups that are most useful for studying symmetric …

Building on earlier papers of several authors, we establish that there exists a universal
constant c> 0 such that the minimal base size b (G) of a primitive permutation group G of …

We investigate connected normal 2-geodesic transitive Cayley graphs Cay (T, S). We first
prove that if Cay (T, S) is neither cyclic nor K 4 [2], then< a>∖{1}⊆ ̷ S for all a∈ S. Next, as …

We prove a structure theorem for a class of finite transitive permutation groups that arises in
the study of finite bipartite vertex-transitive graphs. The class consists of all finite transitive …

In this paper, we study the structure of finite permutation groups with a transitive cyclic
subgroup. In particular we extend the classification due to W. Feit and GA Jones of the …

Given a permutation group 𝐺, the derangement graph of 𝐺 is the Cayley graph with
connection set the derangements of 𝐺. The group 𝐺 is said to be innately transitive if 𝐺 has a …

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or
semiregular. Interest in this class of groups is motivated by two sources: problems arising in …

On groups with every normal subgroup transitive or semiregular Page 1 Journal of Algebra
319 (2008) 1733–1751 www.elsevier.com/locate/jalgebra On groups with every normal …

A transitive simple subgroup of a finite symmetric group is very rarely contained in a full
wreath product in product action. All such simple permutation groups are determined in this …

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be
regarded as the building blocks of finite transitive permutation groups, and are analogues of …