9 papers · 1 filter
Finite permutation groups with quasi-semiregular elements
Michael Giudici, Luke Morgan, Cheryl E. Praeger
A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in t…
Prime power coverings of groups
Michael Giudici, Luke Morgan, Cheryl E. Praeger
For a finite group with normal subgroup , a subgroup of is an -prime-power-covering subgroup if meets every -conjugacy-class of elements of of prime po…
Finite simple groups have many classes of -elements
Michael Giudici, Luke Morgan, Cheryl E. Praeger
For an element of a finite group , the -class of is the set . We prove that the order of a finite nonabelian si…
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 $…
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…