10 papers
A new infinite family of star normal quotient graphs of twisted wreath type
Eda Kaja, Luke Morgan
We construct the first infinite families of locally arc transitive graphs with the property that the automorphism group has two orbits on vertices and is quasiprimitive on exactly…
Vertex-transitive graphs with local action the symmetric group on ordered pairs
Luke Morgan
We consider a finite, connected and simple graph that admits a vertex-transitive group of automorphisms . Under the assumption that, for all , the local action $…
The NNN-Property of Cyclic Groups
Michael Giudici, Luke Morgan, Yian Xu
A Cayley graph is said to be an NNN-graph if it is both normal and non-normal for isomorphic regular groups, and a group has the NNN-property if there exists an NNN-graph for it. I…
Generalised shuffle groups
Carmen Amarra, Luke Morgan, Cheryl E. Praeger
The mathematics of shuffling a deck of cards with two "perfect shuffles" was brought into clarity by Diaconis, Graham and Kantor. Here we consider a generalisation of this pro…
The distinguishing number of quasiprimitive and semiprimitive groups
Alice Devillers, Scott Harper, Luke Morgan
The distinguishing number of $G \leqslant \sym(Ω)$ is the smallest size of a partition of such that only the identity of fixes all the parts of the partition. Extending ear…
Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size, and Minimal Degree
Luke Morgan, Cheryl E. Praeger, Kyle Rosa
In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size,…